Presentation on theme: "Finite Element Method CHAPTER 9: FEM FOR 3D SOLIDS"— Presentation transcript:
1 Finite Element Method CHAPTER 9: FEM FOR 3D SOLIDS for readers of all backgroundsG. R. Liu and S. S. QuekCHAPTER 9:FEM FOR 3D SOLIDS
2 CONTENTS INTRODUCTION TETRAHEDRON ELEMENT HEXAHEDRON ELEMENT Shape functionsStrain matrixElement matricesHEXAHEDRON ELEMENTUsing tetrahedrons to form hexahedronsHIGHER ORDER ELEMENTSELEMENTS WITH CURVED SURFACES
3 INTRODUCTIONFor 3D solids, all the field variables are dependent of x, y and z coordinates – most general element.The element is often known as a 3D solid element or simply a solid element.A 3D solid element can have a tetrahedron and hexahedron shape with flat or curved surfaces.At any node there are three components in the x, y and z directions for the displacement as well as forces.
4 TETRAHEDRON ELEMENT3D solid meshed with tetrahedron elements
5 TETRAHEDRON ELEMENTConsider a four node tetrahedron element
6 Shape functionswhereUse volume coordinates (Recall Area coordinates for 2D triangular element)
7 Shape functions Similarly, Can also be viewed as ratio of distances (Partition of unity)since