Automatic Calculation of Structures

Recommended Prerequisites

Mathematical analysis, algebra and numerical methods. They also should have knowledge of computer programming, elasticity, strength of materials, formulation of solid mechanics problems and their resolution by the finite element method

Teaching Methods

The theoretical contents of the curricular unit will be presented through lectures illustrated with practical cases. Students are encouraged to apply the competences acquired through practical activities associated with the training of using a finite element program, including the analysis and discussion of results. The sharing of professional experience will be encouraged during these activities.

The assessment includes the presentation and discussion of proposed assignments (20%-30%) and a Frequency/Exam (80%-70%).

Learning Outcomes

This course aims to provide an overview of numerical models that can be used in modeling several structural components such as bars, shafts, beams, membranes, plates and shells. It also seeks to highlight the role of numerical modeling based on finite element method, to support decision making and improving the quality of the project. At the end of this course, students should be able to:

 1) Identify the various kinematic models that can be used in the FEM;

 2) Understanding the relevance and specificity of finite elements that can be used in a commercial FE program;

 3) Know and use a commercial FE program in solving structural problems: static, dynamic, unstable, transient analysis.

 4) To analyze the numerical results obtained on the basis of any modeling, and try to find alternative solutions.

Work Placement(s)

No

Syllabus

Part I: Models of reticulate structures, models of plan States, models of plates, shells and three-dimensional structures. Shell equation equilibrium: cylindrical shell; spherical shell. Shell tensions.

Numerical aspects of programming: methods for solving systems of algebraic equations, numerical integration. Generic formulation of a general nonlinear dynamic problems based on the finite element approach: Methods for solving nonlinear problems. Problems of dynamics: modal analysis and transient analysis. Analysis of instability.

Part II. Practices in computational mechanics: Troubleshooting simple bars, beams, plates and shells. Solution of dynamic problems: modal analysis and transient analysis. Solution of instability problems. Practical training how to exchange information between a CAD and a finite element program.

Head Lecturer(s)

Ana Paula Bettencourt Martins Amaro

Assessment Methods

Assessment
Resolution Problems: 30.0%
Exam: 70.0%

Bibliography

1] Neto, M.A.; Amaro, A.; Roseiro, L.; Cirne, J.; Leal, R., Engineering computation of structures: the finite element method. Springer, 2015

[2] Bathe K.-J., Finite Element Procedures in Engineering Analysis, Prentice-Hall,     New Jersey, 1982.

[3] Zienkiewicz,O.C. and Taylor,R.L., The Finite Element Method, Volume I and II, Mac-Graw Hill Book Company, 1991.

[4] Hinton E. and Owen D. R. J., An Introduction to Finite Element Computations, Pineridge Press Int., Swansea, 1986.

[5] Hinton E. and Owen D. R. J., Finite Element Programming, Academic Press, 1977

[6] Mota Soares C. A., Elementos Finitos em Mecânica dos Solidos, Relatorio M 1.82.03, IST, Lisboa, 1982.

[7] Mota Soares, Carlos A. ; Teorias e Análises de Cascas: Métodos Analiticos e Aproximados; CEMUL, Relatório M1.82.02, IST, Lisboa, 1982.

[8] Ugural A., Stresses in Plates and Shells, McGraw-Hill, 2nd ed, 1999.

[9] A Finite Element Primer, Nafems, 1992