FEM Modeling - Introduction to Finite Elements - Lecture Slides, Slides of Mathematical Methods for Numerical Analysis and Optimization

Download FEM Modeling - Introduction to Finite Elements - Lecture Slides and more Slides Mathematical Methods for Numerical Analysis and Optimization in PDF only on Docsity! 1 MANE 4240 & CIVL 4240 Introduction to Finite Elements Practical considerations in FEM modeling Reading assignment: Logan Chap 7 + Lecture notes Summary: • Aspect ratio and element shapes • Use of symmetry • Natural subdivisions at discontinuities • Stress equilibrium in FEM solutions © 2002 Brooks/Cole Publishing / Thomson Learning™ Figure 7-1a (a) Beam with loading: effects of the aspect ratio (AR) illustrated by the five cases with different aspect ratios Aspect ratio = longest dimension/ shortest dimension Aspect ratio and element shapes © 2002 Brooks/Cole Publishing / Thomson Learning™ Figure 7-1b (b) Inaccuracy of solution as a function of the aspect ratio (numbers in parentheses correspond to the cases listed in Table 7-1) © 2002 Brooks/Cole Publishing / Thomson Learning™ Figure 7-2 Elements with poor shapes Avoid abrupt changes in element sizes Abrupt change in element size Gradual change in element size Docsity.com 2 Examples of how NOT to connect elements © 2002 Brooks/Cole Publishing / Thomson Learning™ Figure 7-3 Use of symmetry applied to a soil mass subjected to foundation loading (number of nodes = 66, number of elements = 50) (2.54 cm = 1 in., 4.445 N = 1 lb) Use of symmetry in modeling © 2002 Brooks/Cole Publishing / Thomson Learning™ Figure 7-4 Use of symmetry applied to a uniaxially loaded member with a fillet © 2002 Brooks/Cole Publishing / Thomson Learning™ Figure 7-5 Problem reduction using axes of symmetry applied to a plate with a hole subjected to tensile force Natural subdivisions at discontinuities Look before you leap! 1. Check the model that you have developed: • Boundary conditions • Loadings • Symmetry? • Element aspect ratios/shapes • Mesh gradation 2. Check the results • Eyeball • Anything funny (nonzero displacements where they should be zero?) • Are stress concentrations in places that you expect? • Comparison with known analytical solution/literature 3. If you remesh the same problem and analyze, do the solutions converge? (specifically check for convergence in strain energy) Docsity.com