Presentation on theme: "Finite Element Method CHAPTER 9: FEM FOR 3D SOLIDS"— Presentation transcript:
1Finite Element Method CHAPTER 9: FEM FOR 3D SOLIDS for readers of all backgroundsG. R. Liu and S. S. QuekCHAPTER 9:FEM FOR 3D SOLIDS
2CONTENTS INTRODUCTION TETRAHEDRON ELEMENT HEXAHEDRON ELEMENT Shape functionsStrain matrixElement matricesHEXAHEDRON ELEMENTUsing tetrahedrons to form hexahedronsHIGHER ORDER ELEMENTSELEMENTS WITH CURVED SURFACES
3INTRODUCTIONFor 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.
4TETRAHEDRON ELEMENT3D solid meshed with tetrahedron elements
5TETRAHEDRON ELEMENTConsider a four node tetrahedron element
6Shape functionswhereUse volume coordinates (Recall Area coordinates for 2D triangular element)
7Shape functions Similarly, Can also be viewed as ratio of distances (Partition of unity)since