Finite element method for structural design

Structural analysis is based on formulations of solid mechanics problems that are amenable to numerical processing. It came into being at the same time as the finite element method, from which it is virtually indissociable.
The aim of the course is to train students in structural analysis methods: development of structural models, discretization of models, calculation of elementary vectors and matrices, resolution procedures. The presentation of these concepts and methods is mechanical.

- I - General concepts: Elementary nodal forces and element equilibrium. Elementary nodal displacements and deformation compatibility. Material behavior. Elementary stiffness matrix, rank, physical significance. Change of reference frame. - II - Displacement method : Elementary location matrix. Node equilibrium matrix. Overall structure stiffness matrix. Physical meaning of terms. Technique for assembling elementary vectors and matrices. - III - Beam theory - IV - Elementary stiffness matrices for 2D beam models: Introduction: nodal forces and nodal displacements in bending, shortcomings of the method used for the bar element. Bernoulli model. Shear model. Use of 4 ddl elements. Bernoulli model + tension. Span loads. - V - Integral forms in structural analysis: Reminder of the equations of 3D mechanics, Application of the general technique of weighted residuals to establish the principles of virtual work. - VI - Solving continuous problems using Gallerkin's method - VII - Mathematical preliminaries to M.E.F. Nodal interpolation (Lagrange and Hermite). Interpolation of geometry (change of integration variable in 1D and 2D (calculation of J , detJ and J-1) and change of derivation operator). Numerical integration. M.E.F. convergence - VIII - M.E.F. in structural analysis. - IX - Construction of wire elements - X - Construction of elements for plane problems

Materials and Structures