Structures: Subjects and Syllabuses
Code: CIV2133 | credits: 3
EMENTA
PROGRAMME
BIBLIOGRAPHY
Code: CIV2109 | credits: 3
EMENTA
Introduction to experimental analysis; displacement, deformation and force sensors; digital image correlation; charging systems; characterization of materials by tensile, flexion and torsion tests; characterization of the viscoelastic behavior of materials; characterization of laminates (two materials); experimental analysis of buckling of columns and beams; dynamic experimental analysis Instrumentation and experiments in reinforced concrete structures.
PROGRAMME
1. Behavior scales. Material behavior. Review of elasticity concepts. Stress and deformation states. Constitutive relations. Types of sensors and quantities to be measured.
2. Basic vocabulary in metrology. Electrical resistance strain gauges. Wheatstone jumpers. Application of extensometers and dial indicators in bending problems.
3. Mechanical testing machines and types of loading control: force and displacement. Clip-gage load cells and sensors. Systems flexibility and compliance curve. Concepts of composite materials and their characterization by traction in different orientations.
4. Typical strain gauge rosettes and arrangements. Shear characterization through torsion tests.
5. Least squares method for property adjustment. Rheological models for creep characterization. Lever beams and strategies for creep testing. Factors influencing results.
6. Types of displacement transducers: mechanical, resistive and inductive. Laminate instrumentation and testing. Assessment of the interaction between components.
7. Concepts about digital image correlation (CID). Deformation fields in elements with discontinuities. Application of CID to tension bars with opening.
8. Concepts about instability of beams and columns. Influence of imperfections and residual stresses. Lateral braking and importance of boundary conditions. Southwell chart to obtain critical load. Obtaining resistance curves. Instrumentation and analysis of 2nd order effects in structural systems.
9. Basic concepts about experimental dynamic analysis. Techniques for power supply, instrumentation and data acquisition in dynamic tests. Modal decomposition and natural frequencies. Free and forced vibrations.
10. Instrumentation in reinforced concrete elements. Comparison between theoretical and experimental models. Identification and description of failure modes.
BIBLIOGRAPHY
Freddie, A.; Olmi, G.; Cristofolini, L. Experimental Stress Analysis for Materials and Structures, Springer International Publishing, 2015; Dally, J.W. Experimental Stress Analysis, McGraw-Hill College, 672 pp., 1991; Sutton, MA; Orteu, JJ; Schreier, H.W. Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications, Springer, 2010.
Code: CIV2102 | credits: 3
EMENTA
Linear transformations between systems of generalized forces and displacements. Energy theorems. Curved bars with variable inertia in plane and space. Consideration of deformation due to shear stress. Generic loads. Application to lattice structures. Flexibility and rigidity methods. Consideration of ball joints, springs and inclined supports. Computational implementations. Introduction to the finite element method.
PROGRAMME
- Introduction; stiffness matrix of a truss element; properties of a stiffness matrix. Energy theorems (Clapeyron, Betti, Maxwell, Castigliano), principle of virtual works. Exercises.
2. Mathematical and graphical representation of a curved bar with variable inertia in space, considering deformations due to normal force and shear: flexibility matrix, displacements caused by a generic load, including temperature variation. Calculation of support reactions and equivalent nodal loading. Particularizations for straight beam. Development of tables for corbels. Exercises.
3. Displacements in frames due to temperature variations and support settlements. The concept and procedures for evaluating nodal loading equivalent to distributed loading. Exercises.
4. General formulation of the force method for loading, support settlements and temperature variation, including representation of results. Exercises.
5. Formulation of the displacement method for frames, in general, using the concept of direct stiffness and in the context of a computational code. Exercises.
6. Complete development of a computational code for flat frames, considering inclined supports, hinges and springs. Methods for proper consideration of supports. Graphical representation of the results. Techniques for optimal storage of the stiffness matrix and resolution of the system of equations, including the concept of “skyline” and vectorized storage. Introduction to the finite element method. Exercises.
BIBLIOGRAPHY
BREBBIA, CA; TELLES, JCF; WROBEL, L.C. Boundary element techniques: theory and application in engineering, New York: Springer Verlag, 464 pp., 1984; BEN-ISRAEL, A.; GREVILLE, T.N.E. Generalized Inverses: theory and applications, 2nd. ed., New York: Robert E. Krieger Publ. Co., 395 pp., 2002; WASHIZY, K. Variational methods in elasticity and plasticity, 2nd ed. New York: Pergamon Press, 540 pp., 1973; DOMINGUEZ, J. Boundary elements in dynamics, New York: Elsevier Appl. Science, 707 pp., 1993; SLADEK, V., SLADEK, J. (eds). Singular integrals in boundary element methods, Southampton, UK: Computational Mechanics Publication, 425 pp., 1998; ENGELS, H. Numerical quadrature and cubature, London: Academic Press, 441 pp., 1980; DUMONT, NA Miscellaneous technical articles, Class notes.
Code: CIV2124 | credits: 3
EMENTA
Introduction to design using the limit state method. Structure performance function. Ultimate limit states. Service limit states. Structural reliability. Second order elastic structural analysis. Differential equation of behavior in the plane. Plate resistance. Inelastic buckling and post-buckling resistance of plates. Shear stresses in thin-walled sections. Twisting in tubular sections and type I sections. Warping. Saint-Venant principle. Combination of torsional and bending efforts. Deformations and warping constants. Initial imperfections. Maximum compressive stress. Effective area. Compression in doubly symmetric and monosymmetric profiles. Beams not laterally braced. Lateral buckling with torsion in doubly symmetric and monosymmetric sections. Cantilever beams. Beam-columns in the elastic regime. Resistance of beams-columns in the plane. Out-of-plane beam-column strength. Lateral buckling with torsion in beam-columns formed by doubly symmetrical and monosymmetrical sections.
PROGRAMME
1. Introduction to the limit state method. Concept of structural reliability. Structure performance function. Ultimate and service limit states. Second order structural analysis in the linear regime. Exercises.
2. Differential equation of in-plane behavior in beam elements. Boundary conditions. Exercises.
3. Local buckling of plates. Plate resistance. Inelastic buckling and post-buckling resistance of plates. Concepts of effective width and maximum tension. Exercises.
4. Shear stresses in thin-walled sections. Twisting into tubular sections. Torsion in type I sections. Warping stresses. Saint-Venant principle. Combination of torsional and bending efforts. Exercises.
5. Deformations and warping constants. Shear center in doubly symmetric and monosymmetric profiles. Moment of inertia when warping. Effects of non-uniform twist on warping. Exercises.
6. Initial imperfections. Maximum compressive stress. Axial elastic buckling forces. Effective area. Compressive strength of doubly symmetric and monosymmetric profiles. Exercises.
7. Beams not laterally braced. Lateral buckling with torsion in doubly symmetric and monosymmetric sections. Effect of non-uniform moments. Cantilever beams. Exercises.
8. Beam-columns in the elastic regime. Resistance of beams-columns in the plane. Out-of-plane beam-column strength. Influence of boundary conditions on beam-columns. Lateral buckling with torsion in beam-columns formed by doubly symmetrical and monosymmetrical sections. Exercises.
BIBLIOGRAPHY:
GALAMBOS, TV, Guide to Stability Design Criteria for Metal Structures, 5th ed, John Willey & Sons Inc., 944 pp., 1998 LI, G.; LI, J. Advanced Analysis and Design of Steel Frames, John Willey & Sons Inc., 368 pp., 2007; SALMON, CG; JOHNSON, J.E. Steel Structures Design and Behavior: Emphasizing Load and Resistance Factor, 5th ed., Pearson Inc., 896 pp, 2008; Canadian Standards Association, CSA S16-19: Design of steel structures, 9th ed, 307 pp., 2019; American Institute of Steel Construction, ANSI/AISC 360-16: Specification for structural steel buildings, 15th ed., 680 pp., 2016; CHEN, W. F.; Kim, S. LFRD Steel design using advanced analysis (New directions in civil engineering), CRC Press Inc., 464 pp., 1997.
Code: CIV2125 | credits: 3
EMENTA
Design using the limit state method. Mixed structural systems for commercial and residential buildings. Effective width of the slab. Plastic neutral line. Shear connectors. Mixed trellises. Transverse and longitudinal shear. Resistance of composite beams using solid slabs and composite slabs (steel-deck). Type floor joist system stub-girder. Design resistance to compression of composite columns. Design strength of composite beams-columns. Simplified method for calculating composite beams-columns. Plate girders. Locking and bracing projects. Design strength of slender web beams. Analysis of structures in the plastic regime.
PROGRAMME
- Review: Design using the limit state method. Ultimate and service limit states. Second order structural analysis in the linear regime. Exercises.
2. Composite beams. Design and construction criteria. Effective width of the slab. Plastic neutral line in mixed sections. Shear connectors. Total and partial interaction. Design strength of composite beams. Exercises.
3. Floor joist systemstub-girder. Design and construction criteria. Simplified analysis model. Design resistance of stub-girders. Exercises.
4. Mixed columns. Design and construction criteria. Resistance assessment of composite columns: general method and simplified method. Exercises.
5. Plate girders. Design and construction criteria. Plate girders welded. Plate girders inverted. Components. Rigidity. Draft amendments in plate girders. Applications. Exercises.
6. Design of locking and bracing. Supporting columns. Selection of locks based on the required locking force. Propping of multiple parallel members. Exercises.
7. Slender core beams. Calculation resistant bending moment in slender web beams. Exercises.
8. Introduction to plastic analysis of structures. Elastic, elasto-plastic and rigid-plastic models. Plasticity relationships. Plastic ball joints. Exercises.
BIBLIOGRAPHY
CHIEN, EYL; RITCHIE, J.K., Design and Construction of Composite Floor Systems, Canadian Institute of Steel Construction, 324 pp., 1984; LI, G.; LI, J. Advanced Analysis and Design of Steel Frames, John Willey & Sons Inc., 368 pp., 2007; SALMON, CG; JOHNSON, J.E. Steel Structures Design and Behavior: Emphasizing Load and Resistance Factor, 5th. ed., Pearson Inc., 896 pp., 2008; Canadian Standards Association, CSA S16-19: Design of steel structures, 9th ed., 307 pp., 2019; American Institute of Steel Construction, ANSI/AISC 360-16: Specification for structural steel buildings, 15th ed., 680 pp. 2016; CHEN, W. F.; KIM, S. LFRD Steel design using advanced analysis (New directions in civil engineering), CRC Press Inc., 464 pp., 1997; EUROCODE 4. EN 1994. Design of Composite steel and concrete structures, Part 1.1: General rules and rules for Buildings, CEN – European Committee for Standardization, 121 pp., 2001; EUROCODE 3, EN 1993: 1.3. Design of Steel Structures: General rules for cold-formed thin gauge members and sheeting, CEN – European Committee for Standardization, 93 pp., 2002; GALAMBOS, TV, Structural Members and Frames, Dover Publications, 400 pp., 2016; ADAMS, PF; KRENTZ, HA; KULAK, GL; Limit States Design in Structural Steel, Canadian Institute of Steel Construction, 303 pp., 1986
Code: CIV2126 | credits: 3
EMENTA
Safety principles and durability requirements; Basic and advanced properties of constituent materials; Normal and tangential requests; Connecting rod and tie method and its application to special cases; Aspects of detailing; Service limit states; Structural analysis; Instability and 2nd order effects; Shells and slabs.
PROGRAMME
1. Fundamental behavior of concrete structures. Basic concepts about probabilistic methods. Limit State Method. Useful life and deterioration mechanisms. Requirements for durability and degradation models.
2. Composition and properties of concrete: compression, traction, fracture, multiaxial state, cracked state, aggregate engagement and effects of time. Steel properties. Constitutive models of materials.
3. Simple tensile, compression and bending behavior. Behavior stages. Rupture domains. Moment-curvature relations. Simplified models for sizing and general cases. Compression reinforcement and beams with other geometries. Straight and oblique compound bending behavior. Construction and use of dimensional and dimensionless interaction diagrams. Normal-momentum-curvature relations
4. Shear behavior and stress path in beams. Failure modes and transfer mechanisms in beams without/with stirrups. Scale effect. Cutting analysis and sizing models. Saint-Venant torsions and warping (elastic and in reinforced concrete beams). Models for twisting. Combined efforts. Twists of balance and compatibility.
5. Plasticity theorems. Regions B and D. Considerations on the design of strut and tie models. Criteria for sizing nodes, connecting rods and tie rods. Applications to wall beams, consoles, beams with openings, concentrated loads and others.
6. Adhesion between components. Adhesion laws and failure modes. Anchor lengths. Bar splices. Decaling of traction force. Distribution of tensile reinforcement in section and staging. Anchoring in supports. General recommendations for transverse reinforcement. Pillar armor.
7. Cracking mechanism and models. Convergence cracks and skin armor. Shear cracks. Models for beam deflection. Long-term deformations. Influence of shear on deflections.
8. Structural behavior. Plastic ball joint. Models for analysis with redistribution of efforts: non-linear and plastic. Mohr's analogy. Equilibrium, instability and beam-column theory. Local 2nd order analysis: approaches with standard pillar and general method with/without creep. Global 2nd order analysis: simplified and p-delta methods.
9. Shell sizing (general case). Analysis and design of slabs using elastic and plastic methods. Behavior and analysis of slabs without beams. Punching in slabs. Progressive collapse.
BIBLIOGRAPHY
WIGHT, J.K.; MACGREGOR, J.G. Reinforced Concrete: Mechanics and Design, 7th Ed. Pearson, 1168 pp., 2016; DA SILVA, RC; GIONGO, J.S. Connecting Rods and Tie Models Applied to Reinforced Concrete Structures, EESC-USP, 202 pp., 2000; MENDES NETO, F. Advanced Structural Concrete – Cross Section Analysis under Compound Normal Bending, PINI, 176 pp., 2010; SCHLAICH, J.; SCHAEFER; K.; JENNEWEIN, M. Toward a consistent design of structural concrete, PCI Journal, 32(3), 74-150. 1987; LEONHARDT, F.; MÖNNIG, E. Concrete constructions, Interciência, 1978.
Code: CIV2127 | credits: 3
EMENTA
Introduction: general concepts, classification and types of prestressing. Safety of prestressed concrete structures: actions, types of loading, safety conditions. Materials: concrete, prestressing steel and new materials. Bending: analysis of stresses, pressure lines, limit zones for prestressing cables, verification of section resistance, design sequence. Continuous beams: bending, cable routing. Prestressing losses: friction losses, concrete creep and shrinkage losses, steel relaxation losses. Shear in beams, slabs and adhesion. Areas of regularization of prestressing stresses. Slabs.
BIBLIOGRAPHY
Naaman, A.E. Prestressed Concrete Analysis and Design, 3rd edition, Techno Press 3000, 1176 p., 2012; Hamilton, H.R. Prestressed Concrete: Building, Design, and Construction, Springer, 475p., 2019; Mitchell, D. Prestressed Concrete Structures, Pearson College Div., 1991; Lyn, T.Y.; Burns, N.H. Design of Prestressed Concrete Structures, third edition, Wiley, 646p., 1991
Code: CIV2108 | credits: 3
EMENTA
Deterministic analysis. Free and forced vibration: damped and undamped; transient and persistent vibration of linear systems with one and several degrees of freedom. Response spectra for linear systems subjected to impulsive and periodic excitations. Vibration of continuous systems. Applications to simple systems.
PROGRAMME
I- Dynamics of discrete linear systems with one degree of freedom
Introduction. Equations of motion.
Damped and undamped free vibrations.
Forced vibrations due to harmonic and periodic loads.
Vibration isolation.
Response to any load, full of Duhamel.
Numerical analysis.
II- Dynamics of discrete systems with n degrees of freedom
Equations of motion
Natural frequencies and natural modes of vibration.
Free vibration.
Forced vibration.
Response spectrum.
Equation of motion in matrix form.
Modal analysis.
III-Continuous systems
Beam equations of motion. Eigenvalues and eigenfunctions.
Free and forced vibration.
Approximate methods: Ritz, Galerkin.
BIBLIOGRAPHY
CHOPRA, AK Dynamics of structures, Pearson Education India, 2007; MEIROVITCH, L. Elements of vibration analysis, McGraw-Hill, 1975; CRAIG Jr, RR and KURDILA, AJ Fundamentals of structural dynamics, John Wiley & Sons, 2006; BENAROYA, H. Mechanical vibration: analysis, uncertainties and control, CRC Press, 2004; RAO, S.S. Vibration of continuous systems, John Wiley & Sons, 2019; MEIROVITCH, L. Computational methods in structural dynamics (Vol. 5), Springer Science & Business Media, 1980; CLOUGH, RW, PENZIEN, J. Dynamics of Structures, McGraw-Hill, New York, 1994
Code: CIV2121 | credits: 3
EMENTA
Probability theory review. Analysis in the frequency domain. Random processes: definition and characterization. Differentiation and integration. Weakly stationary processes. Power spectrum and power spectrum density function. Gauss, Poisson and Markov distribution. Distribution of Rayleigh and Vanmarcke peaks. Analysis of systems with one and several degrees of freedom. Linear systems. Approximate methods for analyzing nonlinear systems. Classic probabilistic risk and reliability analysis. Applications to simple systems.
BIBLIOGRAPHY
Maymon, G. Structural Dynamics and Probabilistic Analysis for Engineers, Butterworth-Heinemann, 488p., 2008; Lin.YK, Probalistic Theory of Structural Dynamics, Krieger, 1976. Lin, YK, Cai, GQ, Probabilistic Structural Dynamics: Advanced Theory and Applications, McGraw-Hill, 1994. Clough, R. W., Penzien, J., Dynamics of Structures, McGraw-Hill, 1993. Newland, DE, An Introduction to Random Vibrations: Spectral and Wave Analysis, Addison-Wesley Longman, 1996. Vlasta Molak, Fundamentals of Risk Analysis and Risk Management, Lewis Publishers, 1996. Melchers, RE, Structural Reliability, John Wiley & Sons, 1987.
Code: CIV2119 | credits: 3
Code: CIV2130 | credits: 3
EMENTA
Introduction to composite materials; Micromechanics of a blade; Macromechanics of a laminate; Resistance criteria for composite materials; Aging and durability; Fracture, fatigue and creep; Behavior of structural elements; Connections; Structural systems.
PROGRAMME
1. Behavior scales. Joint behavior of materials. Definition of composite materials and design philosophy. Constituents: materials, forms and functions. Types of composites and mechanical behavior. Manufacturing and applications.
2. Review of elasticity concepts. Constitutive matrices of isotropic, orthotropic and anisotropic laminae. Engineering properties. Rule of mixtures and other approaches.
3. Micromechanical approach to resistance: traction and compression. Experimental characterization and other failure modes. Biaxial resistance criteria. Progressive collapse and strength prediction in laminates.
4. Influencing factors and water absorption models. Influence of temperature: post-curing, glass transition and decomposition. Hygro-thermo-mechanical models. General model for aging analysis.
5. Basic concepts of fracture mechanics. Models with cohesive elements. Mechanisms of initiation and propagation of a fatigue crack. Fatigue degradation models. Fluency concepts. Rheological models. Viscoelasticity of composite materials.
6. Global stiffness parameters of linear structural elements. Behavior of beams and pillars; influence of shear deformations, local and global instabilities and resistance. Behavior and sizing of sandwich panels.
7. Types of connections. Bolted and glued connections: force/stress distribution and failure modes. Models for predicting semi-rigid behavior.
8. Structural systems with composite materials. Strategies for ductility. Concepts for structural analysis with redistribution of efforts. Dimensioning of elements according to existing standards.
BIBILOGRAPHY
JONES, R.M. Mechanics of Composite Materials, 2nd ed., CRC Press, 538 p., 2018; BARBERO, E.J. Introduction to Composite Materials, 3rd Ed., CRC Press, 570p., 2017; BANK, L.C. Composites for Construction: Structural Design with FRP Materials, John Wiley & Sons, 551p., 2006; GIBSON, R.F. Principles of Composite Material Mechanics, 4th ed., CRC Press, 700p., 2016
Code: CIV2801 | credits: 3
EMENTA
Two-dimensional graphics system architectures. Programming in the MATLAB environment. Introduction to object-oriented programming and event-driven programming. Development of interactive graphic programs. Handling mouse events on canvas. Graphical and interactive analysis of lattice and continuous structures in the MATLAB environment.
PROGRAMME
- Introduction to MATLAB.
2. Cross process for analyzing continuous beams in MATLAB.
3. Introduction to object-oriented programming.
4. Drawing vector primitives on canvas in MATLAB.
5. Programming in event-driven interface systems.
6. Two-dimensional graphics system architectures.
7. Geometric transformations in the plane.
8. MATLAB AppDesigner environment for creating GUI (Graphics User Interface) applications.
9. Handling mouse events.
10. Development of graphic-interactive application programs for lattice and continuous structures in the MATLAB environment.
BIBLIOGRAPHY
Martha, L.F. Matrix Analysis of Object-Oriented Structures, Editora GEN LTC and Editora PUC-Rio, 352p., 2018.; Chapman, S.J. MATLAB Programming for Engineers, 2002; Azevedo, E.; Conci, A. Computer Graphics – Image Generation, volume 1, Editora Campus, 2003; Conci, A.; Azevedo, E. Computer Graphics – Theory and Practice, volume 2, Editora Campus, 2007; Gomes, JM; Old, L. CG, volume 1, Computing and Mathematics Series, IMPA, 1998; Rogers, D. F., Adams, J. A. Mathematical Elements for Computer Graphics, second edition, McGraw-Hill International editions, Computer Series, New York, 1990; Rogers, D.F. Procedural Elements for Computer Graphics, McGraw-Hill International editions, Computer Series, New York, 1985.; Foley, J.D.; Van Dam, A.; Feiner, S.; Hughes, J. Computer Graphics: Principles and Practice, second edition in C, Addison-Wesley, 1995; Cox B.; Novobilski A. Object-oriented programming: an evolutionary approach, Addison-Wesley, Upper Saddle River, NJ, 1991; Fish, J.; Belytschko, T. A First Course in Finite Elements, John Wiley & Sons, 2007.
Code: CIV2106 | credits: 3
EMENTA
Structure stability theory: Basic concepts and definitions. Stability criteria: static, dynamic and energetic criteria. Physical and geometric non-linearity; equilibrium trajectories. Limit and bifurcation points. Critical and post-critical behavior; sensitivity to imperfections. Multiple bifurcations and modal coupling. Vibrations of structural elements susceptible to buckling. Structural stability problems: Stability of slender, elastic columns. Plate stability. Shell stability. Stability of beams and frames in the plane. Buckling of beams in space. Stability of arches and rings. Systems under non-conservative loads. Stability of inelastic systems. Computational modeling of stability problems: Approximate methods: Ritz, Galerkin, etc. Eigenvalue problems in stability and use of finite elements. Geometric matrices for the various structural elements. Analysis of non-linear systems; identification of limit and bifurcation points and obtaining equilibrium trajectories.
PROGRAMME
I- STRUCTURE STABILITY THEORY
Basic concepts and definitions.
Stability criteria: static, dynamic and energetic criteria.
Physical and geometric nonlinearity; equilibrium trajectories.
Limit and bifurcation points.
Critical and post-critical behavior; sensitivity to imperfections.
Multiple bifurcations and modal coupling.
Vibrations of structural elements susceptible to buckling.
II-STRUCTURAL STABILITY PROBLEMS
Stability of slender, elastic columns.
Stability of plates and shells.
Stability of beams and frames in the plane.
Buckling of beams in space.
Stability of arches and rings.
Systems under non-conservative loads.
Stability of inelastic systems.
III- COMPUTATIONAL MODELING OF STABILITY PROBLEMS
Approximate methods: Ritz, Galerkin, etc.
Eigenvalue problems in stability and use of finite elements.
Geometric matrices for the various structural elements.
Analysis of nonlinear systems; identification of limit and bifurcation points and obtaining equilibrium trajectories.
BIBLIOGRAPHY
CROLL, JGA; WALKER, A.C. Elements of structural stability, John Wiley & Sons, 1972.; BRUSH, DO; ALMROTH, BO; Hutchinson, J.W. Buckling of bars, plates, and shells, McGraw-Hill, 1975; CEDOLIN, L.; BAZANT, Z.P. Stability of Structures, Dover Science, 1014p., 2003; THOMPSON, JMT; HUNT, G.W. Elastic instability phenomena, John Wiley & Sons, 1984; ALLEN, HG; BULSON, P.S. Background to buckling, McGraw-Hill, 1980; COOK, R.D.; MALKUS, DS; PLESHA, ME; WITT, R.J. Concepts and applications of finite element analysis, John Wiley & Son, 2007; TIMOSHENKO, SP; GERE, J.M. Theory of elastic stability, Courier Corporation, 2009; ZIEMIAN, RD (Ed.) Guide to stability design criteria for metal structures, John Wiley & Sons, 2010
Code: CIV2153 | credits: 3
EMENTA
Basic review of tensor analysis and continuum mechanics. Elasticity problems with large displacements. Total, Updated and Corotational Lagrangian Formulation. Geometric nonlinear analysis of truss and beam structures. Solution of systems of nonlinear equilibrium equations. Formulation of the finite element method for large displacements in continuous media. Nonlinear behavior of materials. Introduction to the contact problem. Computational implementation of a nonlinear finite element program.
PROGRAMME
Presentation of nonlinear problems. Analytical solution of nonlinear problems with one degree of freedom. Review of concepts of continuum mechanics and tensor analysis. Balance trajectories. Continuation methods. Methods for detecting critical points.
Total and Updated Lagrangian Formulation. Geometric nonlinear analysis of trusses. Development of a nonlinear truss analysis program. Co-rotational Formulation. Nonlinear beam elements. 2D and 3D finite element formulation for geometric nonlinearity. Materials with non-linear elastic and elastoplastic behavior. Incorporation of plastic behavior into a finite element program. Integration of tensions. Introduction to the contact problem. Methods of treating contact conditions. Computational implementation of the Finite Element Method for continuous media. Modeling and analysis of structures.
BIBLIOGRAPHY
CRISFIELD, M. Non-Linear Finite Element Analysis of Solids and Structures: Advanced Topics, John Wiley & Sons, 1997; BATHE, K.-J. Finite Element Procedures, Klaus-Jürgen Bathe, second edition, 1043p., 2014; BELYTSCHKO, WK, LIU, WK and MORAN, B. Nonlinear Finite Elements for Continua and Structures, John Wiley and Sons, 2000
Code: CIV2110 | credits: 3
EMENTA
Code: CIV 2118 | credits: 3
EMENTA
Introduction to the Finite Element Method: objectives, history, general idea and classical applications. Direct Stiffness Method. Basic notions of finite element modeling. Weak formulation for one-dimensional problems: Rayleigh-Ritz Method, Weighted Residual Method, Principle of Stationary Potential Energy. Variational formulation for bar and beam elements. Variational formulation for linear and quadratic triangular and quadrangular elements. Numerical integration. Isoparametric formulation. Three-dimensional elements. Convergence conditions. Problems and limitations of the finite element method. Special elements and applications. Computational implementation.
PROGRAMME
Introduction to the Finite Element Method: objectives, history, general idea and classical applications. Direct Stiffness Method. The concept of discretization of a continuous medium. Basics of finite element modeling: natural and essential boundary conditions, meshes, aspect ratio of elements, model symmetry considerations. Weak FEM formulation for one-dimensional elements: Rayleigh-Ritz Method, Weighted Residual Method. Principle of stationary potential energy. Manipulation of commercial finite element programs. Exercises.
Variational formulation of the Finite Element Method: bar element, beam element. Elements of Continuum Mechanics: formulation in displacements. 2D formulation: triangular and quadrangular elements in a plane stress state. 3D elements: tetrahedra and main applications. Numerical integration: Newton-Cotes and Gauss quadrature formulas. Isoparametric formulation. Jacobian analysis. MEF convergence conditions. Special elements and applications. Problems involving the solution of finite elements: shear locking and hourglass effect. Exercises. Computational implementation of the Finite Element Method: general structure of a finite element program. Development of a finite element program for linear elastic problems.
BIBLIOGRAPHY
COOK, R., MALKUS, D.; PLESHA, M. Concepts and Applications of Finite Element Analysis, 4th edition, John Wiley & Sons, 2002; FELIPPA, CA Introduction to Finite Element Methods, lecture notes from the course Introduction to Finite Elements Methods (ASEN 5007), Department of Aerospace Engineering Sciences, University of Colorado at Boulder, 2009.; LOGAN, D.L. A First Course in the Finite Element Method, 5th edition, Cengage Learning, 2011; Fish, J.; BELYTSCHKO, T. A First Course in Finite Elements, John Wiley & Sons, 2007; ZIENKIEWICZ, OC, TAYLOR, RL; ZHU, J.Z. The Finite Element Method, Its Basis & Fundamentals, 6th edition, Elsevier, 2005.; SZABO, B.; BABUSKA, I. Introduction to Finite Element Analysis, John Wiley & Sons, 1991.
Code: CIV 2151 | credits: 3
EMENTA
PROGRAMME
BIBILOGRAPHY
Code: CIV2101 | credits: 3
EMENTA
PART II: (a) Origin of differential equations, classification and nomenclature and first order equations. (b) Second order ordinary differential equations with constant coefficients – homogeneous and non-homogeneous, (c) systems of linear equations, (d) resolutions by series, orthogonal polynomials and stability.
PART III: Initial value and boundary value problems. Partial differential equations: mathematical physics equations (Laplace, wave, heat, etc.). Variable separation method; boundary conditions and initial conditions.
PART IV: Variational calculus: Euler equation. The delta operator. Functionals with several functions and derivatives of any order. Natural and forced boundary conditions. Lagrange constraints and multipliers. Variational principles of mechanics. Functionals with two or more independent variables.
Code: CIV2123 | credits: 3
EMENTA
Code: CIV2129 | credits: 3
EMENTA
Code: CIV2802 | credits: 3
EMENTA
Introduction to Computer Graphics for Engineering. Introduction to Object Oriented Programming. Two-dimensional visualization with OpenGL. 2D geometric transformations and Window-Viewport transformation. Color and pattern handling from the OpenGL graphics library. Programming in an event-driven interactive graphical environment. Canvas mouse events. Digital representations of curves. Introduction to Computational Geometry. Two-dimensional region weaving. Line segment intersection algorithms. Computational geometry predicates: proximity test and point inclusion. Finite element mesh generation: mapping algorithms, boundary pushing algorithms and Delaunay triangulation algorithms. Geometric transformations for 3D visualization. 3D camera model and 3D view control.
PROGRAMME
1. Presentation of the Visual Studio and Qt development environment.
2. Development of a simple program with the environment: sum of two numbers.
3. Development of an RPN calculator.
4. Introduction to Object Oriented Programming.
5. Two-dimensional visualization with OpenGL.
6. 2D geometric transformations and Window-Viewport transformation.
7. Color and pattern treatment of the OpenGL graphics library.
8. Programming in an event-driven interactive graphical environment.
9. Qt signals & slots paradigm.
10. Canvas mouse events.
11. Digital representations of curves.
12. Introduction to Computational Geometry.
13. Weaving of two-dimensional regions.
14. Line segment intersection algorithms.
15. Computational geometry predicates: proximity test and point inclusion.
16. Finite element mesh generation: mapping algorithms, boundary advancement algorithms and Delaunay triangulation algorithms.
17. Geometric transformations for 3D visualization.
18. 3D camera model and 3D view control.
19. 3D camera model and 3D view control.
BIBLIOGRAPHY
Stroustrup, B. C++ The Programming Language, Bookman Company, 3rd edition, 2000; Celes, W. Introduction to Data Structures – With C Programming Techniques, 2nd edition, Editora Gen-LTC, 438p., 2016; Azevedo, E.; Conci, A. Computer Graphics – Image Generation, volume 1, Editora Campus, 2003; Conci, A.; Azevedo, E. Computer Graphics – Theory and Practice, volume 2, Editora Campus, 2007; Gomes, JM; Old, L. CG, volume 1, Computing and Mathematics Series, IMPA, 1998.
Code: CIV2103 | credits: 3
EMENTA
PROGRAMME
Code: CIV2104 | credits: -3
EMENTA
Basic equations of the theory of elasticity. Plasticity for uniaxial stress states, isotropic and kinematic hardening. Solution of nonlinear systems of equations. Implementation of a computer program for elastoplastic trusses. Theory of Continuous Damage Mechanics (one-dimensional). Plasticity for 2D and 3D problems. Classic models of plasticity. Numerical methods for solving initial value problems. Numerical implementation of an elastoplastic model in a finite element program. Algorithmic tangent (consistent). Numerical models for strong discontinuities: cohesive interface model, XFEM, embedded fractures.
PROGRAMME
- Basic concepts of the theory of elasticity, plasticity, viscoelasticity, damage and fracture. Applications.
2. One-dimensional plasticity: isotropic and kinematic hardening models, internal variables, mathematical description of the uniaxial plasticity problem. Development of a computer program for elastoplastic analysis of hardened trusses.
3. Solution of the nonlinear equilibrium problem. Continuation methods: load control, displacement control, arc length, convergence conditions. Implementation.
4. Continuous damage mechanics theory: representative element of volume, isotropic damage, plasticity and damage association. Implementation and application to the truss problem.
5. Plasticity for general stress states. Mathematical formulation of the plasticity model with isotropic and kinematic hardening/softening. Main classic models, plastic surfaces, and their representations. Solution of the local initial value problem. Stress projection algorithms and plastic state calculation. Convergence and stability criteria. Algorithmic tangent (consistent). Application to plasticity J2. Computational implementation of an elastoplastic model in a finite element program.
6. Models for representing strong discontinuities (fractures): cohesive interface models, XFEM models, embedded fracture models. Applications to almost brittle materials such as concrete and rocks
BIBLIOGRAPHY
SIMO JC; Hughes, T.J.R. Computational Inelasticity, New York: Springer Verlag, 392 p., 1998; DE SOUZA NETO, EA; PERIC, D.; OWEN, D.R.J. Computational Methods for Plasticity, United Kingdom, John Wiley & Sons, 791 p., 2008; LEMAITRE, J. A Course on Damage Mechanics, Spinger Verlag Berlin Heidelberg, 225 p., 1992; LUBLINER, J. Plasticity Theory, MacMillan, 495 p., 1990; BONET, J.; WOOD, R.D. Nonlinear Continuum Mechanics for Finite Element Analysis, 2nd edition, Cambridge University Press, 318p., 2008
Code: CIV2105 | credits: 3
EMENTA
PROGRAMME
BIBLIOGRAPHY
Code: CIV2112 | credits: -3
EMENTA
PROGRAMME
BIBLIOGRAPHY
Code: CIV2122 | credits: 3
EMENTA
Code: CIV2191/2192 | credits: 3
EMENTA
The subject Special Topics in Structures does not have a pre-defined syllabus, as it aims to provide an opportunity to delve deeper into topics linked to research lines and projects.
Code: CIV2195/2195 | credits: 3
EMENTA
The subject Special Topics in Structures does not have a pre-defined syllabus, as it aims to provide an opportunity to delve deeper into topics linked to research lines and projects.
Code: CIV2195/2195 | credits: 3
EMENTA
The subject Special Topics in Structures does not have a pre-defined syllabus, as it aims to provide an opportunity to delve deeper into topics linked to research lines and projects.
Code: CIV2174 | credits: 1
EMENTA
The subject Special Topics in Structures does not have a pre-defined syllabus, as it aims to provide an opportunity to delve deeper into topics linked to research lines and projects.
Code: CIV2176 | credits: 3
EMENTA
The subject Special Topics in Structures does not have a pre-defined syllabus, as it aims to provide an opportunity to delve deeper into topics linked to research lines and projects.
Code: CIV2177 | credits: 3
EMENTA
The subject Special Topics in Structures does not have a pre-defined syllabus, as it aims to provide an opportunity to delve deeper into topics linked to research lines and projects.
Code: CIV2171 | credits: 2
EMENTA
The subject Special Topics in Structures does not have a pre-defined syllabus, as it aims to provide an opportunity to delve deeper into topics linked to research lines and projects.
Code: CIV2174 | credits: 1
EMENTA
The subject Special Topics in Structures does not have a pre-defined syllabus, as it aims to provide an opportunity to delve deeper into topics linked to research lines and projects.
Code: CIV2179 | credits: 3
EMENTA
The subject Special Topics in Structures does not have a pre-defined syllabus, as it aims to provide an opportunity to delve deeper into topics linked to research lines and projects.