Slide_Chpt-Modelling_Techniques有限元课件.ppt

The Finite Element Method MODELLING TECHNIQUES CONTENTS INTRODUCTION CPU TIME ESTIMATION GEOMETRY MODELLING MESHING Mesh density Element distortion MESH COMPATIBILITY Different order of elements Straddling elements CONTENTS USE OF SYMMETRY Mirror symmetry Axial symmetry Cyclic symmetry Repetitive symmetry MODELLING OF OFFSETS Creation of MPC equations for offsets MODELLING OF SUPPORTS MODELLING OF JOINTS CONTENTS APPLICATIONS OF MPC EQUATIONS Modelling of symmetric boundary conditions Enforcement of mesh compatibility Modelling of constraints by rigid body attachment IMPLEMENTATION OF MPC EQUATIONS Lagrange multiplier method Penalty method INTRODUCTION Ensure reliability and accuracy of results. Improve efficiency and accuracy. INTRODUCTION Considerations: Computational and man power resource that limit the scale of the FEM model. Requirement on results that defines the purpose and hence the methods of the analysis. Mechanical characteristics of the geometry of the problem that determine the types of elements to use. Boundary conditions Loading and initial conditions CPU TIME ESTIMATION To create an FEM model with minimum DOFs by using elements of as lower dimension as possible, and To use as coarse a mesh as possible, and use fine meshes only for important areas. GEOMETRY MODELLING Reduction of complex geometry to a manageable one. 3D? 2D? 1D? Combination? GEOMETRY MODELLING Detailed modelling of areas where critical results are expected. Use of CAD software to aid modelling. Can be imported to FE software for meshing. MESHING To minimize the number of DOFs, have fine mesh at important areas. Element distortion Use of distorted elements in irregular and complex geometry is common but there are some limits to the distortion. The distortions are measured against the basic shape of the element Square ? Quadrilateral elements Isosceles triangle ? Triangle elements Cube ? Hexahedron elements Isosceles tetrahedron ? Tetrahedron elements Element distortion