Finite Element Methods for Structural Analysis

COURSE CONTENT  

• Presentation of the generalized theoretical framework for the numerical analysis of deformable solids and structures. Transition from the analytical equations of stress equilibrium to weak formulations of the equations of equilibrium and approximate methods of solutions. Methods of weighted residuals, trial functions, the concept of global and local approximation of displacements. Variational formulations of the equilibrium equations, the Galerkin method, the method of arbitrary (virtual) displacements.
• Expansion of the finite element methods to 3D problems of deformable solids. Basic families of volume finite elements and their shape functions
• Analysis of beam and frame structures. Finite elements of classical bending, the concept of C¹ contntinous shape functions and finite elements. Finite elements of bending with shear (Timoshenko beams). Frame elements.
• Simplified three-dimensional elements for the analysis of thin-wall structures and aeronautical structures. Membrane, Plate and Shell finite elements.
• Non-linear finite element structural analysis. Introduction to key types of structural nonlinearity, admissible variational forms of the equilibrium equations. Iterative methods of solution of the nonlinear system. Total and tangential stiffness matrices. Analysis of structures with material nonlinearity. Analysis of geometrically nonlinear structures. Structural instability and buckling. The problem of initial or linear buckling. Prediction of stable pre- and post-buckling response.
• The course is combined with laboratory seminars and exercises which include programing of finite element software, and linear and nonlinear FE structural analyses of plate/shell structures.

LEARNING OUTCOMES 

This an advanced course on the topics of finite element methods, computational structural mechanics and numerical structural analysis.  Upon completion of the course, the students are anticipated to:

• Attain advanced knowledge in the Method of Finite Elements, Numerical Structural Analysis and computational structural mechanics.
• Obtain experience and knowledge in the analysis of complex three dimensional (structures, with focus on the analysis of thin-wall 3D structures (frames, plates, shells)
• Obtain basic knowledge on the non-linear analysis of structures, iterative/incremental methods of solution, the cases of material nonlinearity, geometric nonlinearity and buckling analysis.
• Acquire skills and hands-on experience in the development, programming and evaluation of finite element software.
• Acquire skills and hand-on experience on the static analysis of complex structures in the linear and nonlinear regime.