Finite Element Analysis Investigative Methods in Engineering Naveed Hussain INVESTIGATIVE METHODS Engineering Problem Analytical Approach Experimental Approach Numerical Approach 1- ANALYTICAL METHODS • Solve a mathematical model than a physical model • Models consist of a set of mathematical equations such as differential equations etc. • In most cases, complex equations are insolvable • Solutions often contain infinite series, special functions…. • Little hope in predicting many phenomenon of practical interest. ANALYTICAL METHODS - EXAMPLE Question: If we apply a force on a solid, what are the values of the displacements, stresses, and strains at EACH MATERIAL POINT? ANALYTICAL METHODS - EXAMPLE Exact solution ο MISSION IMPOSSIBLE To answer this question, we need to solve the following equations: Equations for solving linear solid mechanics problem We need to solve a problem consisting of total 15 equations, among which 9 equations are partial differential equations !! 2 - NUMERICAL METHODS Approximate solution ο Numerical methods • • • Finite Element Method (FEM) – Structural/Stress analysis Finite Volume Method (FVM) – Fluid flow/ Heat and mass transfer Finite Difference Method (FDM) – Thermal and fluid problems The Finite Element Method (FEM), an approximation to reality, is a numerical technique to find approximate solutions of partial differential equations. πΉπΉ = πΎπΎ ππ How Does FEA Work? Physical problem Change physical problem Improve mathematical model Mathematical model Numerical model Does answer make sense? YES! Happy ο No! Refine analysis Design improvements Structural optimization How Does FEA Work? Finite Element Analysis – General procedure FUSION 360 ABAQUS/CAE ANSYS Workbench MS Excel MATLAB ANSYS NASTRAN ABAQUS ANSYS MARC How Does FEA Work? – Example Submitted for Analysis Fixed boundary Uniform loading, 10N/mm2 Elastic Modulus, E=210kN/mm2 Poisson’s Ratio, Cantilever steel plate ππ=0.3 Linear Static Analysis Problem: Obtain the displacements and stresses in the plate 1- Deformations/Displacements MSC PATRAN Node Pre-processing Geometry ο ο Meshing Meshing Boundary conditions ο Boundary Conditions Loading conditions ο Loading conditions Material properties ο Solutiontype type ο Solution Element 2 - Von-Mises Membrane stresses How Does FEA Work? – More examples 1- Side-impact crashworthiness 2- Font end BMW crash showing the dummy strike to the airbag 3 - EXPERIMENTAL METHODS • Most reliable information about a physical process often obtained by measurement • Full scale tests: Expensive and often impossible • Extrapolation of results: General rules not available • Measurements/Uncertainties: Many situations present serious difficulties, and instruments are not free from error • In cases prohibited: Safety or environmental issues EXPERIMENTAL METHODS – EXAMPLE Mechanical test in the structures lab to look at fatigue and crack propagation in steel girders SUMMARY Engineering Problem Analytical Approach Experimental Approach Numerical Approach • Mathematical model • Suitable for simple problems • Simplifications and assumptions • Insolvable differential equations • For both new and known Algebraic equations phenomenon Advanced computers Results faster and at low cost • Cannot be fully replaced • Experimentation leads Reduce the number of and computation follows experiments • For known phenomenon • • • • Thank you for your attention!
