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Analysis and Design of Structures

The core of the courses comes from the Structural Engineering Department of the School of Civil Engineering of NTUA  in collaboration with the Geotechnical Department of the same School and with the partnership of the School of Applied Mathematics and Physical Sciences, of the School of Electrical and Computer Engineering and the School of Mining and Metallurgical Engineering of NTUA.  

In order to obtain the Postgraduate Diploma, students must attend and be successfully examined at 10 courses, five (5) in the winter and five (5) in the spring semester, as well as develop a Postgraduate Thesis.

Of these ten (10) courses, four (4) must be from the elective direction, three (3) must be from the Geotechnical course category, and three (3) from the Analysis course category.


Direction A
Structural Engineering


Direction B
Analysis and Design of Earthquake Resistant Structure


Geotechnical courses


Analysis courses

A.  Structural Engineering

Selection of 4 courses in case the specific direction has been chosen.

101Advanced Concrete TechnologyE. BadogiannisCVWinter36
102Design Models for Aseismic Repair and Strengthening
(not available in academic year 2023-2024)
E. VintzilaiouCVWinter36
103Design of Steel Buildings D. Vamvatsikos,
I. Vayas
104Recent Advances in RC Design ModelsE. Vougioukas,
M. Kotsovos
105Reliability of Structures C. Trezos CVWinter36
106Steel Structures for Marine ApplicationsCh. Gantes,
P. Thanopoulos
107Advanced Mechanics of MansoryE. VintzilaiouCVSpring36
108Design of Cable and Membrane StructuresCh. GantesCVSpring36
109Design of Technical Projects II J. ErmopoulosCVSpring36
110Information Systems in Construction ManagementJ-P. PantouvakisCVSpring36
111Engineering MaterialsG. FourlarisMMMSpring36

B.  Analysis and Design of Earthquake Resistant Structure

Selection of 4 courses in case the specific direction has been chosen.

201Nonlinear Analysis of Frame Structures and
Applications in Seismic Engineering
Μ. Fragiadakis,
S. Diamantopoulos
202Novel Methods for Seismic Isolation and
Response Control of Structures
A. SextosCVWinter36
203Signal Processing in Earthquake EngineeringΜ. FragiadakisCVWinter36
204Engineering SeismologyD. Vamvatsikos,
A. Sextos,
O. Ktenidou
205Experimental Earthquake EngineeringCh. MouzakisCVSpring36
206Pathology and Design of Structures under Seismic ActionsC. SpyrakosCVSpring36
207Special Topics in Earthquake Engineering
(not available in academic year 2023-2024)
C. Spyrakos,
I. Psycharis
208Structural Intervention on Cultural Heritage StructuresΜ. Fragiadakis, C. Spyrakos, 
E. Toumpakari, I. Psycharis

Geotechnical courses

Selection of 3 courses.

301Computational Geomechanics
(not available in academic year 2023-2024)
A. ZervosCVWinter36
302Geotechnical Engineering in Design of StructuresV. Georgiannou,
A. Zervos
303Ground Investigation MethodsV. Marinos,
Ch. Saroglou,
A. Antoniou
304Computational Methods in the Analysis
of Underground Structures
M. KavvadasCVSpring36
305Seismic Design of Surface and
Underground Geotechnical Structures
A. Papadimitriou,
G. Bouckovalas

Analysis courses

Selection of 3 courses.

401Advanced Plastic Analysis of Framed StructuresK. SpiliopoulosCVWinter36
402Advanced Structural DynamicsM. Nerantzaki,
I. Katsikadelis
403Applied Structural Analysis of Framed and Shell Structures
(not available in academic year 2023-2024)
E. SapountzakisCVWinter36
404Design of Technical Projects IE. Sapountzakis,
L. Stavridis
405Theory of ShellsV. KoumousisCVWinter36
406Mechanics of a Continuous MediumA. GiannakopoulosAMPSWinter36
407Machine LearningA.G. Stafylopatis, G. Stamou,
A. Voulodimos, P. Tzouveli
408Boundary ElementsG. TsiatasCVSpring36
409Load-carrying Behavior and Design of Structural SystemsL. StavridisCVSpring36
410Non Linear Finite Analysis of StructuresV. Papadopoulos,
K. Spiliopoulos
411Stochastic Finite ElementsV. PapadopoulosCVSpring36
412 Structural OptimizationN. Lagaros,
S. Triantafyllou,
V. Koumousis
413Applied ElasticityG. Exadaktylos,
P. Gourgiotis
414Plasticity and Fracture of MaterialsA. GiannakopoulosAMPSSpring36

101. Advanced Concrete Technology
Introduction : Concrete materials, Cement, types and production methods. Selection of the cement. Aggregates properties and their influence on concrete performance. Water, additive materials, admixtures. Fresh concrete. Strength (Compressive, tensile) resistance to cyclic loading, fatigue, strength under uniaxial, biaxial and triaxial loading. Factors affecting the strength of concrete. Durability of concrete and design, Corrosion of reinforcement, Service life of RC structures. Shrinkange, Elasticity, Creep. High performance concrete. Mixing, transportation, casting, compaction, curing. Special concretes. In lab and in situ quality control. Concrete standards and regulations.
Instructor: E. Badogiannis
Assistant: K. Tsivolas, A. Feretzakis

102. Design Models for Aseismic Repair and Strengthening
Short historical review / Inspection / Measurements / Assessment of available bearing capacity/ The logic of the intervention-categories and criteria/ Design actions and partial safety factors/ Constitutive laws of force transfer mechanisms across interfaces (Triaxial compression, Friction, Pullout, Dowel action)/Shear capacity of interfaces/ The target of redesign (performance levels and critical behavior values)/Available plastic rotation/ Theory and redesign applications (using steel or FRPs): Increase of bending capacity/increase of shear capacity/inadequate overlap length/increase of local ductility/infill shear walls/new shear walls.

Instructor: E. Vintzilaiou

103. Design of Steel Buildings
Design of singly story steel buildings,
Design of singly story steel buildings,
Dissipative Structural systems for Seismic Resistance,
Loads on Buildings 

Instructors: D. Vamvatsikos, I. Vayas
Assistants: G. Dougka, Ch. Lachanas

104. Recent Advances in RC Design Models
Concrete behaviour: Strength, stress-strain behaviour under short-term loading, cracking, failure mechanism.
Behaviour of structural concrete elements: Modes of failure, causes of failure, physical model of element behaviour.
Design of structural concrete elements: Compressive force path method, earthquake-resistant design, application of the method for the design of beams, columns, structural walls, slabs, frames, etc.

Instructors: E. Vougioukas, M. Kotsovos

105.  Reliability of Structures
Introduction, probabilistic vs deterministic design of structures. Basic notions on probabilities. Central limit theorem. Distributions. Estimation of parameters. Maximum likelihood. Transformations. Regression analysis. Return period. Monte Carlo simulation (independent and correlated variables). Probabilistic models of resistances. Probabilistic models of actions (wind, snow, earthquake, self-weight). Combination of actions. Time varying actions, fatigue. Stochastic processes. Probability of failure, Level II method. Safety index. Reliability of serial and parallel systems. Bayes theorem, updating prior information reliability of existing structures. Code format, partial safety factors. Probabilistic design of special structures. Conformity criteria.

Instructor: C. Trezos

106. Steel Structures for Marine Applications
The course consists of three parts.
The course introducing the students to issues pertaining to the behavior, analysis and design of marine and offshore structures, with emphasis on steel structures.
The course covers issues of configuration of structural systems for various types of steel structures for marine applications (jetties for loading/unloading, offshore platforms, offshore wind turbines), optimum member sections, types of connections between members, relation between selection of structural system and method of erection, numerical modeling issues (software selection, types of elements, mesh density, modeling of connections), analysis methods (static vs. dynamic, linear vs. nonlinear, interpretation of results), dimensioning (concept of limit state design verifications, design criteria, failure criteria, member verifications, buckling lengths, connection verifications,fatigue), construction drawings (general layout, assembly, part and erection drawings).
Instructors: Ch. Gantes, P. Thanopoulos
Assistant: S. Gkatzogiannnis

107. Advanced Mechanics of Masonry
Technology of old and modern masonry.
Behaviour of masonry in compression, in tension, in shear
(Out-of-plane) Buckling and bending of plain, confined and reinforced masonry
The Mechanics of tie-beams (timber or RC)
Behaviour of interfaces within masonry. Mechanisms of load transfer (friction between mortar and stone or brick, pullout/push-in, dowel action)
Methods of analysis of masonry structures
In situ assessment of mechanical properties of historic masonry
Pathology of masonry structures
Assessment of residual properties of masonry
Intervention materials and techniques
Design and redesign models for masonry

Instructor: E. Vintzilaiou

108. Design of Cable and Membrane Structures
The course introducing the students to issues pertaining to the behavior, analysis and design of tension structures.
The objectives of the course are multiple: (a) to understand the peculiarities of behavior and analysis of such structures, due to their lack of compressive, shear and bending stiffness, and their resulting flexibility to transverse loads, which leads them to nonlinear behavior, (b) to present their significant advantages for covering large spans, either in roofs or in bridges, (c) to address technological issues regarding their materials of construction, connections, the importance and ways of application of pretension and the erection methods, and (d) to be introduced to design methods of structures including cables and membranes: individual cables, guyed towers, suspended and cable-stayed bridges, cable roofs, cable nets, prestressed and air-supported membranes.
Instructor:  Ch. Gantes
Assistant: S. Gkatzogiannnis

109. Design of Technical Projects II
Planning of development projects. Procedures for design, construction, and supervision. Total quality and environmental planning. Bridge axis alignment, selection, and arrangement of spans. Structural morphology and systems of concrete and steel bridges. Design actions in highway, railway, and pedestrian bridges. Cable suspended bridges, aerodynamic considerations. Special topics on steel bridges (Orthotropic deck, Fatigue etc.). Bearing and expansion joints. Design of bridge piers and abutments, protection against scouring. Design methods of concrete bridges (slab bridges, T-beam girders, box girders). Aseismic design of bridges. Design for environmental effects. Modern construction methods.

Instructor: J. Ermopoulos
Assistant: J. Sigalas

110. Information Systems in Construction Management
Overview of information systems in construction management. Review of construction management as an information processing system (techniques, procedures, Books of Knowledge (BoKs), Contract types). Review of time scheduling methodologies (MPM, linear methods, simulation, critical chain, monte carlo), Use of commercial systems (Primavera, MS-Project, Excel, 4D systems). Information Systems Analysis and Design Techniques (Data bases, Systems Analysis, Systems Design). IT & telecommunications applications in construction management (PDA's, wearable computers, wireless & satellite networks, project websites, e-site, e-construction, document control systems).

Instructor: J-P. Pantouvakis

111. Engineering Materials
Classes of materials: Metals and alloys, ceramics, polymers and composite materials. Technological evolution and trends, properties and cost comparison, main applications.
Structure-properties relationships: Nature of chemical bonding, crystal structure and imperfections, dislocations. Solidification of metals. Mechanical properties and their dependence on the microstructure. Hardness, tensile strength, ductility, toughness, strain hardening, recovery and recrystallization. Fracture mechanisms, elements of fractography. Impact strength, transition from ductile to brittle fracture.
Other properties: Fatigue and fretting fatigue. Creep. Wear resistance. Corrosion and high temperature oxidation. Protection against corrosion (coatings, anodic and cathodic protection).
Study of some common alloys: Iron and steel, cast iron, aluminium and light alloys, copper alloys.
Production and processing methods and their relation to mechanical properties: Casting, hot and cold forming, powder metallurgy. Defects, inclusions, texture and anisotropy.
Welding: Welding methods, welding joints, welding defects and non destructive methods.
Construction steels: Plain carbon and low-alloy steels. High elastic limit steels, dual phase steels, controlled rolling and microalloyed steels. Stainless steels. Steels for low temperature applications.
Reinforced concrete steels: Types and relevant mechanical properties. Resistance to high temperatures. Weldability and welding techniques.

Instructor: G. Fourlaris

201. Nonlinear Analysis of Frame Structures and Applications in Seismic Engineering
1st Part: Introduction – algorithms for solving non-linear problems
Introduction and types of non-linear problems,
Introduction to algorithms for solving non-linear problems (full and modified Newton-Raphson method, method failures),
Non-linear methods for exceeding limit points (pure incremental solution, displacement control, arc-length),
Solvers and structure of a non-linear analysis code.
2nd Part: Geometric non-linearity
Geometrically non-linear mesh element
Kinematic relations of a beam in the plane (corotational theory)
Geometrically non-linear beam element
Application to solving buckling problems of structures.
3rd Part: Introduction to material non-linearity
Introduction to non-linear simulations for the inelastic analysis of structures
Comparison of the step-by-step method with the Newton-Raphson method 
Uniaxial constitutive laws in terms of stress-strains (σ-ε): (a) bilinear s-e relation, (b) kinematic, isotropic and mixed hardening, (c) constitutive relations for steel and concrete
Phenomenological simulations in terms of torque-rotation (M-φ) (Clough-Johnston, Takeda models, stiffness and strength reduction)
Cross-sectional analysis: (a) moment-axial interaction plots, (b) curvature moment plots
Lumped plasticity 
Fiber elements displacement & force elements
Spatial frames - torsion
Simulation of shear
Simulation of diaphragm
4th unit: Non-linear dynamic analysis and applications
The Newmark method for nonlinear dynamic problems
The mass matrix (lumped, consistent mass matrix)
Formulation of damping matrix (The problem of spurious moments in the case of models of concentrated plasticity).
Convergence and accuracy of non-linear dynamic problems
Non-linear dynamic analysis using seismic records.
Instructors: Μ. Fragiadakis, S. Diamantopoulos

202. Novel Methods for Seismic Isolation and  Response Control of Structures
1. Introduction to seismic isolation (recap from UG course)
Development of Seismic Isolation Worldwide. Theoretical Basis of Seismic Isolation. Seismic response of Seismic Isolated Hospitals during the Feb. 6th, 2023 Turkey earthquake sequence.
2. Isolation System Components (recap from UG course)
Mechanical Characteristics and Numerical Modeling of Isolators. Advanced FEM aspects. Software example: Seismostruct
3. Code Provisions for Seismic Isolation.
Review of new generation North America, Asian and European Seismic Codes.
4. Ground Motion Selection for Seismically Isolated systems
Design Earthquake Ground Motion Selection and Scaling for SI
5. Design of a new SI building
Worked Example: Stavros Niarchos Foundation complex (Library and Opera buildings)
6. Design of a SI bridge 
Worked example: Egnatia Highway overpass
7. Redesign and seismic upgrade of existing R/C buildings with SI.
Worked example: Multi-storey R/C building including cost/benefit comparison with conventional redesign 
8. Redesign and seismic upgrade of existing URM buildings with SI.
Worked Example: Rehabilitation of the Theological School of Chalki using multiple layer SI 
9. Geotechnical and Low-Cost Seismic Isolation methods for low-income regions.
Worked Example: A school building in Nepal founded on PVC-sand-PVC sliding foundation system
10. In class tutorial 
11. Novel control methods
Novel passive, semi-active, active and hybrid mass dampers for buildings in seismic regions. Limitations of control systems.
12. Coupled seismic isolation and control systems
Coupled systems of geotechnical seismic isolation and active damping. Case study: Rion-Antirion bridge
13. Use of TMDs in seismic regions
Tuned mass damper inerter systems for control of buildings subjected to earthquake ground motions. Challenges and limitations.
Instructor: A. Sextos

203. Signal Processing in Earthquake Engineering
The course discusses methods for processing structural response signals.
1) Introduction to signal theory. Autocorrelation and crosscorrelation. 
2) Analysis in the frequency domain, Fourier transform, Power spectrum. 
3) Dynamic response of systems/structures.
4) Signal processing (filtering, baseline correction, spectral leakage, windowing).
5) Transfer function.
6) FRF (frequency Response Function).
7) Properties of signal recording devices (sensors).
8) Short Time Fourier Transform (STFT).
9) The Frequency Domain Decomposition method.
10) Wavelet analysis (Continuous Wavelet Transform).
Instructor: Μ. Fragiadakis
Assistants: H. Gianni, G. Prentzas

204. Engineering Seismology
The lesson of Engineering Seismology presents the following subjects dealing with the estimation of earthquake hazard and loss assessment.
Presentation of regional seismicity, fault description and earthquake source mechanism.
Characteristics and effects of near field ground motions.
New generation attenuation relationships.
Evaluation of seismic hazard.
Site effects on ground motion.
Artificial accelerograms and simulation of near field pulses.
Selection of seismic records for design.
Review of earthquake loss assessment methods.
Presentation of loss assessment HAZUS methodology.
Displacement based loss assessment methods.

Instructors: D. Vamvatsikos, A. Sextos, O. Ktenidou
Assistants: A. Gerontati, K. Mastrodimou

205. Experimental Earthquake Engineering

Instructor: Ch. Mouzakis

206. Pathology and Design of Structures under Seismic Actions
Typical damage to structures from earthquakes and their interpretation. Correlating them with the seismic motion-excitation and the characteristics of the structure. Analysis of the function of the basic structural elements and structural members according to the materials composed of. Correlation of the function of these elements with damping and stiffness. Influence of the position and function of the various members on the final seismic behavior of the structures. Criteria for selecting position, type and operation of the various structural members. Simulation of structures, depending on the material, the function of the member and the geometry of the structure.

Instructor: C. Spyrakos

207. Special Topics in Earthquake Engineering
Principles of seismic design of special structures (e.g. bridges, tanks, dams).
Criteria for the selection of the appropriate structural model.
Displacement based seismic design.
Dynamic soil-structure interaction / methods of analysis and applications.
Dynamic structure-water interaction / methods of analysis and applications to representative systems (dams, tanks).
Principles of seismic design of structures with base isolation / applications.
Seismic assessment of existing structures.
Retrofit and strengthening of structures / methods of analysis and applications.

Instructors:  C. Spyrakos, I. Psycharis

208. Structural Intervention on Cultural Heritage Structures
1. Masonry monuments (dry connection)
This type of monuments include classical-Hellenistic monuments (temples, towers, fortifications, etc.) as well as some prehistoric ones (the most emblematic vaulted tombs), Ottoman (minarets) or more recent ones (parts of monuments, e.g. porches, as well as burial monuments). This module spans 4-5 lessons and includes:
(a) Typology, structural analysis and routine pathology; 
(b) Theoretical approach to structural behavior, methods of analysis, controls etc.,
(c) Planning and dimensioning interventions with reference to principles and regulatory framework, and
(d) Examples of analyzes and interventions.
2. Masonry monuments (with mortars) 
This type of monuments includes Roman, Byzantine, post-Byzantine, Ottoman and newer monuments. This module spans 6-7 lessons and includes: 
(a) Typology of common and special structures, analysis, common pathology and reference to the principles and regulatory framework (materials and typical structures, causes and development of damage, categorization of structures, institutional framework and legislation), 
(b) Methods of investigating an existing situation;
(c) Theoretical approach to structural behavior, simulation and analysis methods (masonry mechanics, simulation methods and linear analysis methods, inelastic static analysis, local mechanisms),
(d) Planning and dimensioning of interventions,
(e) Examples of analyzes and interventions.
3. Supporting lectures (1 or 2 lectures) 
(a) Protection of monuments in practice, in the context of the Archaeological Service and the Ministry of the Interior: history of the protection, preservation and restoration of monuments in Greece,  
(b) Building materials, materials of historical constructions and repair materials (reference to stones & bricks, emphasis on mortars & grouts): brief historical review, methods of analysis and characterization of materials, pathology, determination of repair and reinforcement material requirements (performances), design. 
4. Guest speaker lecture 
It will concern various relevant topics related to the protection of monuments, such as: archaeology, material science, modern methods of recording, security of museum exhibits, etc. In this way, students will obtain an overview on the expertise of other specialties involved in the protection of monuments and archaeological sites.
Instructors: Μ. Fragiadakis, C. Spyrakos, E. Toumpakari, I. Psycharis

301. Computational Geomechanics
1. Introduction to plasticity. Yield function, plastic potential, loading/unloading.
2. The Tresca and von Mises models and their application in modelling undrained clay.
3. The Mohr-Coulomb and Drucker-Prager models, and their application in modelling drained soil behaviour.
4. Integration of the constitutive relations.
5. The concept of critical state. Modified Cam-Clay and its application in modelling soil behaviour.
6. Formulation and solution of seepage problems using finite element analysis.
7. Formulation and solution of transient, coupled pore pressure-deformation (consolidation) problems using finite element analysis.
Instructor: A. Zervos

302. Geotechnical Engineering in Design of Structures
The topics of seepage, compression and consolidation are examined briefly and are related to engineering practice and to current research work. By using an extended case study of the Tower of Pisa as a theme, the concepts can be applied to different soils and the long-term settlement of soil can be assessed. The major challenges facing designers of multi-propped deep excavations, particularly in crowded urban areas are examined. Embedded retaining walls such as secant bored pile walls and diaphragm walls used in the construction of deep sections of retained cuttings and cut-and-cover tunnels in road schemes and excavations in urban cities are studied with emphasis on the stress transfer and deformation mechanisms around diaphragm walls. The study of retaining systems is extended to include reinforced soil retaining walls and/or steepened embankments, as a relatively new cost effective method of construction which reduces embankment width and land-take and is environmentally acceptable. The classic preliminary design methods, including Eurocode 7, are presented both for retaining walls and reinforced soil. By using case studies (e.g. Egnatia Motorway) the Codes of practice are applied through analytical programs. The earthquake loading is assessed for conventional retaining walls, reinforced soil walls and bridge abutments.
Instructors: V. Georgiannou, A. Zervos
Assistants: E. Pavlopoulou, A. Paganis

303. Ground Investigation Methods
General principles and methods of ground investigation. Geological maps and sections. Interpretation of aerial photographs. Sampling drilling for geotechnical purposes, description of samples, preparation of geotechnical sections. In-situ tests for geotechnical purposes (cross-hole, permeability, standard penetration, static penetration, determination of in-situ stresses, direct shear, pressometer and dilatometer tests). Geotechnical monitoring methods for the design and construction of civil engineering works. Fundamentals of the geophysical methods (seismic, electrical and other) with applications in the design and construction of engineering projects.
Instructors: V. Marinos, Ch. Saroglou, A. Antoniou

304. Computational Methods in the Analysis of Underground Structures
Elasto-plastic stress and deformation analysis around circular tunnels. Derivation of elasto-plastic convergence-confinement curves. Analysis of tunnel end-effects (Panet curves). Principles of numerical methods for the analysis of underground structures (modeling of the 3-D problem in 2-D) - rockmass loosening methods (methods of deconfinement and stiffness reduction). Numerical analyses of the excavation and temporary support (staged excavation, temporary support measures) using Finite Element programs (application using the computer program RS2). Analysis of the loading on the permanent support of tunnels. Analysis of face stability and face reinforcement techniques.
Instructor: Μ. Kavvadas
Assistants: D. Georgiou

305. Seismic Design of Surface and Underground Geotechnical Structures
This post-graduate course has the following themes:
1. Introduction to Geotechnical Earthquake Engineering. Basic elements of engineering seismology, with emphasis on strong ground motion.
2. Single degree of freedom structural vibration with base excitation, elastic response spectra.
3. Seismic wave (P, S, Rayleigh, Love) propagation in homogeneous and inhomogeneous soil.
4. Seismic design of underground tunnels and pipelines against seismic waves and permanent ground displacements.
5. Soil amplification (or de-amplification) of seismic ground motion with analytical and numerical methods. Practice with dedicated software.
6. Seismic design of retaining walls with the Mononobe-Okabe method (pseudo-static design) and with Richards-Elms (allowable displacements),
7. Topography effects and seismic design of soil and rock slopes.
8. Liquefaction, with emphasis on assessment methods and on its effects on Civil Engineering works. Description of ground improvement methods and methods for mitigating the effects of liquefaction.

Instructors: A. Papadimitriou, G. Bouckovalas
Assistant: J. Tsiapas

401. Advanced Plastic Analysis of Framed Structures
Introduction to the plastic design of structures. Redistribution of forces. Ductility. Relation with the Codes of Practice. Step-by-step 1st order elastoplastic analysis of frames. Principle of virtual work. Lower and upper bound theorems of plastic collapse. Safe moment distribution. Collapse mechanisms. Holonomic and non-holonomic behaviour. Mathematical programming. Kuhn-Tucker conditions. Linear programming. Simplex method. Mesh and nodal description. Static-kinematic duality. Flow rule. Stable materials. Rigid plastic behaviour. Alternative linear programs of limit analysis. Uniqueness of limit load. Automatic limit load evaluation. Optimal plastic design. Automatic optimal plastic design using linear programming. Variable loading. Alternating plasticity. Incremental collapse. Shakedown. Residual stress. Melan’s theorem. Mesh-unsafe shakedown linear program and automatic shakedown load evaluation. Relation between limit and shakedown load. Elastoplastic analysis with 2nd order effects. Large displacements. Geometric non-linear elasto-plastic stiffness matrix. Arc-length method. Comparison of limit loads with and without 2nd order effects. Merchant-Rankine formula. Inelastic dynamic analysis of MDOF systems. Seismic response of buildings. Ductility ratios. Pounding of buildings. Reference to approximate static methods (pushover, etc.). Practice with commercial packages (SAP, Abaqus, etc.).
The course aims to the in-depth understanding of the inelastic behaviour of framed structures since plasticity is the basis of all today’s Codes of Practice. Emphasis is also put on the mathematical framework and the computational techniques of plastic analysis. In this way the course addresses both the practicing engineer and the researcher.

Instructor: K. Spiliopoulos
Assistant: V. Tsotoulidi

402. Advanced Structural Dynamics
Dynamic loads and dynamic models of structures. Methods of derivation of equations of motions for structural systems (Equilibrium of forces, principle of virtual displacements, Hamilton’s, principle, Langrage equations). Damping (viscous, Coulomb, structural). Discretization of continuous systems. Free and forced vibrations of SDOF systems. The finite element method for beam structures. (plane and space trusses and frames). Rigid bodies in elastic structures. Axial constraints. Free vibrations of MDOF systems. Modal damping, proportional damping. Numerical evaluation of eigenfrequencies and mode shapes. Partially restrained structures. Forced vibrations of MDOF systems. The method of modal superposition. Modal participation, static correction method. Reduction of degrees of freedom (kinematic constraints, Ritz vectors). Support excitation. Response spectrum analysis (ABSSUM, CQC, SRSS). Nonlinear response of structures Numerical solution of the equations of motion in time domain. Dynamic analysis of multi-storey buildings. Base isolation. Applications to civil engineering structures.

Instructors: M. Nerantzaki, I. Katsikadelis
 Assistants: N. Babouskos

403. Applied Structural Analysis of Framed and Shell Structures
The displacement vector of a particle of a body. Components of strain of a particle of a body. Implications of the assumption of small deformation. Traction and components of stress acting on a plane of a particle of a body. Proof of the tensorial property of the components of stress. Properties of the strain and stress tensors. Components of displacements for a general rigid body motion of a particle. The compatibility equations. Equations of equilibrium. Stress-strain relations. Formulation and solution of boundary value problems using the linear theory of elasticity. The principle of Saint-Venant. Prismatic bodies subjected to pure tension. Prismatic bodies subjected to pure bending. Plane stain and plane stress problems in elasticity. Fundamental assumptions of the theories of mechanics of materials for line members. Internal actions on a cross-section of line members. The boundary value problems in the theories of mechanics of materials for line members. The boundary value problem for computing the axial component of translation and the internal force in a member made from an isotropic linearly elastic material subjected to axial centroidal forces and to a uniform change in temperature. The boundary value problem for computing the angle of twist and the internal torsional moment in members made from an isotropic linearly elastic material subjected to torsional moments. Primary and secondary warping functions. Warping normal stresses. The classical theory of beams. Solution of the boundary value problem for computing the transverse components of translation and the internal actions in prismatic beams made from isotropic linearly elastic material. The Timoshenko theory of beams. A displacement and a stress function solution to transverse shear loading of beams. Computation of the shearing components of stress in beams subjected to bending without twisting. Shear center. Theory of plates. Buckling of elastic structures. Nonlinear theory of elasticity.

Instructor: E. Sapountzakis
Assistant: I. Tsiptsis

404. Design of Technical Projects I
Presentation of major bridge projects. Design principles, methods of construction. Design of bridges. 
Static and dynamic models of bridge structures. Slab and continuous body structures.
Static and dynamic models of bridge structures. Slab and beam structures, box shaped bridges.
The grid model for the analysis of bridge structures.
Support of bridge structures and its modelling. Oblique and curved bridges.
Torsional parameters of elements for the analysis of framed structures.
Introduction to thin walled beams. Comparison between open and closed sections.
Analysis of warping due to torsion. Stress state due to the warping restrain.
The concept of bimoment and its relation to the stress state. The basic equation of torsional behavior and its practical treatment through the analogy with the laterally loaded tensioned beam. 
Box-girder bridges. Rectilinear girders under eccentric traffic loading.
Stress-state due to the deformability of cross-section profile under eccentric loading.
Curved box-girders in bridge design. Determination of longitudinal bending and torsional state-of-stress. Lateral response of section walls.
Influence of prestressing on the curved girders of bridges. Reducing the torsional response through prestressing.
Instructors: E. Sapountzakis, L. Stavridis
Assistants: K. Kapasakalis, O. Sapountzaki

405. Theory of shells
Introduction to shell structures. An historical overview. Basic elements of differential geometry. Space curves, parametric representation. Surfaces as grid of families of space curves. First fundamental form. Applications. Assumptions of thin shell theories. Stress resultants per unit length. Equilibrium Equations. The general initial and boundary value problem of theory of shells. Statical indeterminacy of the general problem. Membrane theory assumptions. Cylindrical shells. General solution for the statically determinate problem. Strains and displacements. Applications. Use of symbolic language i.e. Maple or Mathematica for the solution of cylindrical shells for various loading cases and support conditions. Membrane theory of conical shells. Equilibrium equations. General solution. Applications. Use of symbolic language i.e. Maple or Mathematica for the solution of conical shells for various loading cases and support conditions. Membrane theory of Shells of revolution. Equilibrium equations. General solution for axisymmetric loading cases. Spherical Shell. Hyperbolic shells. Applications for open or closed spherical shells. Shells of revolution for arbitrary loading. Fourier series solution, symmetric and antisymmetric cases. Differential geometry notion of curvature. Second fundamental form. Gauss-Godazzi conditions. Bending theory of cylindrical shells. Axisymmetric loading. Beam on elastic foundation type of solution. Donnell theory. Applications for cylindrical shells with different boundary conditions. Comparison with numerical solutions with finite element method. Design provisions of Eurocode 3 for steel thin shell structures.

Instructor: V. Koumousis
Assistant: K. L. Antoniadis

406. Mechanics of a Continuous Medium
Tensor analysis. The Rayleigh transport theorem. The deformation gradient. The polar decomposition theorem. Rotations and stretches. Lagrangian and Eulerian description of deformation metrics. Mass conservation. Conservation of linear momentum. Conservation of angular momentum. The stress tensors: Cauchy, 1st and 2nd Piola-Kirchhoff. Objective deformation measures. The velocity gradient tensor. Decomposition to strain rate and spin. Principal stretches and principal directions. Invariants of symmetric tensors. Orthogonal tensors. Equilibrium equations and the Virtual Work theorem. Constitutive equations in elasticity and fluid mechanics. Anisotropy. Hyperelasticity. Internal constrains: incompressibility, inextensibility. The first thermodynamic theorem. The second thermodynamic theorem. Objective stress rates. Objective deformation rates. Mechanical power and work conjugate stresses and deformation tensors. Jump conditions and discontinuities. Problems of large deformation elasticity. Problems of fluid mechanics.
Instructor: A. Giannakopoulos

407. Machine Learning
Instructors: A.G. Stafylopatis, G. Stamou, A. Voulodimos, P. Tzouveli

408. Boundary Elements
Introduction. Boundary Elements and Finite Elements. Historical development of the BEM. Preliminary Mathematical Concepts. The Gauss-Green theorem. The divergence theorem of Gauss. Green’s second identity. The Dirac delta function. The BEM for Potential Problems in Two Dimensions. Fundamental solution. The direct BEM for the Laplace and the Poisson equation. Transformation of the domain integrals to boundary integrals. The BEM for potential problems in anisotropic bodies. Numerical Implementation of the ΒΕΜ. The BEM with constant boundary elements. The Dual Reciprocity Method for Poisson’s equation. Computer program for solving the Laplace equation with constant boundary elements. Domains with multiple boundaries. The method of subdomains. Boundary Element Technology. Linear elements. Higher order elements. Near-singular integrals. Applications. Torsion of non-circular bars. Deflection of elastic membranes. Bending of simply supported plates. Heat transfer problems. Fluid flow problems. The BEM for Two-Dimensional Elastostatic Problems. Equations of plane elasticity. Betti’s reciprocal identity. Fundamental solution. Integral representation of the solution. Boundary integral equations. Numerical solution of the boundary integral equations. Body forces. Computer program for solving the plane elastostatic problem with constant boundary elements. Applications.

Instructor: G. Tsiatas
Assistant: N. Babouskos

409. Load-carrying Behavior and Design of Structural Systems
Structural behavior and design of steel and reinforced concrete beams
Structural behavior and design of prestressed concrete beams.The treatment of prestressing
Structural behavior of one-story and multistory frames. Gravity loads, Horizontal loads, Lateral stiffness. Juxtaposition of shearing and bending behavior.
The influence of deformations on the structural behavior of beams (Second order theory)
The influence of deformations on the structural behavior of frames (Second order theory)
Structural behavior and design of arches and arch-beam systems
Load-carrying behavior and design of cable prestressed structures
Main characteristics of the structural behavior of grids
Specific topics on the structural action, behavior and design of reinforced and prestressed concrete slabs

Instructor: L. Stavridis

410. Non Linear Finite Analysis of Structures
Issues of continuum mechanics and basic tensor analysis. Introduction to nonlinear analysis. Incremental equations of motion, Green Lagrange strain tensor. Cauchy stress tensor, Piola Kirchhoff stresses, Incremental total and updated Lagrangian formulations. Principle of Virtual work in a non-linear setting. Linearization of non-linear equations of motion and incremental - iterative solution methods. Newton-Raphson algorithm. Path following techniques. Arc-Length. Geometric Non linearity. Finite element method for geometric non – linear problems: Truss and Cable elements, Plane Strain and plane stress elements, Three-dimensional solid elements, Structural elements: beam and general shell elements. Material nonlinearity. Problem statement. Elastoplastic problem in one dimension. Isotropic and Kinematic Hardening. J2 Plasticity. Deviatoric stress. Deviatoric strain. Yield surface. Von Mises & Tresca Yield criteria. Drucker’s postulate. Maximum dissipation principle. Associated and non-associated flow rules. Perfect plasticity. Radial return algorithm. Algorithms for isotropic, kinematic and combined hardening. Algorithmic tangent operator. Finite element method for materially nonlinear problems. Implementation using MSOLVE and Commercial Software. 

Instructors: V. Papadopoulos,  K. Spiliopoulos
Assistants: S. Pirialakos, I. Kapogiannis, V. Tsotoulidi

411. Stochastic Finite Elements
Scope: The course aims at the investigation of the effect of uncertain parameters (material and geometric properties, loading) on structural response variability.
Introduction: Random variables, cumulative distribution function, probability density function, statistical moments (mean value, variance, skewness and kurtosis), covariance. Stochastic processes and fields: Definition, stationary stochastic processes, ergodicity, analysis in the frequency domain-Fourier transform: autocorrelation and spectral density functions, Gaussian stochastic processes. Representation/discretization of stochastic processes and fields using (i) Point discretization methods: midpoint, integration and nodal point methods (ii) Average discretization methods: local average and weighted integral methods (iii) Spectral representation method: simulation of stationary Gaussian stochastic processes and fields. Formulation and solution of the stochastic problem: Stochastic virtual work principle, formulation of the stochastic stiffness matrix using the local average and weighted integral methods, solution by Taylor, Neumann series expansion and by Monte Carlo simulation. Applications: Computer applications on framed structures and 2D elasticity problems: investigation of the effect of several stochastic field parameters (probability distribution, correlation length and autocorrelation function) on structural response variability.

Instructor: V. Papadopoulos 
Assistants: I. Kalogeris, S. Pirialakos

412. Structural Optimization
Basic concepts. Design variables, objectives and constraints. Optimal sizing, shape and topology design problems for skeletal and 2D structures. Continuous and discrete optimal design problems. Methods of mathematical programming. Linear programming problem, simplex method and interior point methods. Nonlinear programming. Approximate methods of solution. Duality principle. Optimality criteria methods, fully stresses design and redesign formulas. Applications with Excel, Fortran and Matlab. Sensitivity analysis, approximate methods. Accuracy and reliability of sensitivity analysis methods. Sensitivity analysis of skeletal and 2D structures analyzed with the finite element method. Direct method of sensitivity analysis. Adjoint method. Applications by using the finite element method computer program NASTRAN. Discrete optimization problems. Some basic problems of integer programming. Dynamic programming, simple applications. Genetic algorithms- evolutionary optimization algorithms. Applications to structural design problems.

Instructors: N. Lagaros, S. Triantafyllou, V. Koumousis
Assistant: A. Stamos

413. Applied Elasticity
Elements of Tensor Analysis. Traction. Stress Tensor. Balance Laws. Equations of Motion and Equations of Equilibrium. Symmetry of Stress Tensor. Strains and Rotations. Equations of Compatibility. Constitutive Elasticity Equations. Strain Energy. Generalized Hooke’s Law. Anisotropy – Isotropy. Navier-Cauchy Equations and Beltrami-Michell Equations. Boundary Conditions. Boundary Value Problems. Two-Dimensional Problems. Plane Strain and Plane Stress. Airy’s Stress Function. Exact Theory of Torsion. Prandtl’s Stress Function. Stress-Concentration Problems. Williams’ Technique. Self-Similar Problems. Flamant-Boussinesq and Kelvin Problems. Contact Problems. Energy Theorems and Methods. Uniqueness Theorem. Principle of Superposition. Rayleigh-Ritz Method. Several Generalizations. Elasticity and Thermodynamics. Wave Propagation. Viscoelasticity. Thermoelasticity. Elements of Fracture Mechanics. Griffith’s Theory – Applications in the Design of Structures.
Instructors: G. Exadaktylos, P. Gourgiotis

414. Plasticity and Fracture of Materials
A. Plasticity of Materials
A.1 Introduction
A.2 Limit analysis - reminders
A.3 Absolutely solid-perfect plastic body
A.4 Elastoplastic analysis
A.5 Rate effects
A.6 Special issues
A.7 Thermodynamics
A.9 Large plastic deformation and rotation
A.8 Cyclic plasticity and low cycle fatigue
B. Breakage of Materials
B.1 Small and large cracks
B.2 Crack analysis with linear elasticity
B.3 Analysis of cracks with nonlinear elasticity and plasticity
B.4 Diffuse micro-cracking and damage parameter
Instructor: A. Giannakopoulos


National Technical University of Athens
9 Heroon Politechneiou,
Zografou GR 15780,
Athens, Greece


Phone: 210 772 3613 
Fax: 210 772 3450