1 MANE 4240 & CIVL 4240 Introduction to Finite Elements FEM Discretization of 2D Elasticity Prof. Suvranu De Reading assignment: Lecture notes Summary: • FEM Formulation of 2D elasticity (plane stress/strain) •Displacement approximation •Strain and stress approximation •Derivation of element stiffness matrix and nodal load vector •Assembling the global stiffness matrix • Application of boundary conditions • Physical interpretation of the stiffness matrix Recap: 2D Elasticity x y S u S T Volume (V) u v x p x p y X a dV X b dV Volume element dV S u : Portion of the boundary on which displacements are prescribed (zero or nonzero) S T : Portion of the boundary on which tractions are prescribed (zero or nonzero) Examples: concept of displacement field x y 3 2 1 4 2 2 Example For the square block shown above, determine u and v for the following displacements x y 1 4 Case 1: Stretch Case 2: Pure shear y 2 2 1/2
FEM Discretization of 2D Elasticity
Jun 12, 2023
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