Peter I. Kattan

The Linear Brick (Solid) Element

The linear brick (solid) element is a three-dimensional finite element with both local and global coordinates. It is characterized by linear shape functions in each of the x, y, and z directions. It is also called a trilinear hexahedron. This is the third isoparametric element we deal with in this book. The linear brick element has modulus of elasticity E and Poisson’s ratio v.

The Linear Tetrahedral (Solid) Element

The linear tetrahedral (solid) element is a three-dimensional finite element with both local and global coordinates. It is characterized by linear shape functions. It is also called the constant strain tetrahedron. The linear tetrahedral element has modulus of elasticity E and Poisson’s ratio v.

The Spring Element

The spring element is a one-dimensional finite element where the local and global coordinates coincide. It should be noted that the spring element is the simplest finite element available. Each spring element has two nodes as shown in Fig. 2.1. Let the stiffness of the spring be denoted by k.

The Space Truss Element

The space truss element is a three-dimensional finite element with both local and global coordinates. It is characterized by linear shape functions. The space truss element has modulus of elasticity E, cross-sectional area A, and length L.

The Space Frame Element

The space frame element is a three-dimensional finite element with both local and global coordinates. The space frame element has modulus of elasticity E, shear modulus of elasticity G, cross-sectional area A, moments of inertia I x and I y , polar moment of inertia J, and length L.

The Quadratic Triangular Element

The quadratic triangular element is a two-dimensional finite element with both local and global coordinates. It is characterized by quadratic shape functions. This element can be used for plane stress or plane strain problems in elasticity. It is also called the linear strain triangle. The quadratic triangular element has modulus of elasticity E, Poisson’s ratio v, and thickness t.

The Quadratic Quadrilateral Element

The quadratic quadrilateral element is a two-dimensional finite element with both local and global coordinates. It is characterized by quadratic shape functions in each of the x and y directions. This element can be used for plane stress or plane strain problems in elasticity. This is the second isoparametric element we deal with in this book. The quadratic quadrilateral element has modulus of elasticity E, Poisson’s ratio v, and thickness t.

The Quadratic Bar Element

The quadratic bar element is a one-dimensional finite element where the local and global coordinates coincide. It is characterized by quadratic shape functions. The quadratic bar element has modulus of elasticity E, cross-sectional area A, and length L.

The Plane Truss Element

The plane truss element is a two-dimensional finite element with both local and global coordinates. It is characterized by linear shape functions. The plane truss element has modulus of elasticity E, cross-sectional area A, and length L.

The Linear Triangular Element

The linear triangular element is a two-dimensional finite element with both local and global coordinates. It is characterized by linear shape functions. This element can be used for plane stress or plane strain problems in elasticity. It is also called the constant strain triangle. The linear triangular element has modulus of elasticity E, Poisson’s ratio v, and thickness t.