Chapter 6 Plane Stress and Plane Strain Stiffness Equations
Introduction
This chapter considers the two-dimensional (planar) finite elements, which are defined by
three or more nodes in a two-dimensional plane (that is, x-y). The two-dimensional element i

Chapter 3
Development of Truss Equations
Introduction
To derive the stiffness matrix for a bar element.
To illustrate how to solve a bar assemblage by the direct stiffness method.
To introduce guidelines for selecting displacement functions.
To descri

Dynamic and Modal Analysis
Dynamics of a Spring-Mass System
Spring-mass system subjected to a time-dependent force
In above figure, the single-degree-of-freedom spring-mass system subjected to a
time-dependent force
F (t ) as shown. Here k represents the

Chapter 15 Thermal Stress
In addition to the strains associated with the displacement functions due to mechanical loading,
there are strains within a body due to temperature variation. We will discuss about the stresses
and strains due to temperature vari

Abaqus Three-Dimensional Solid Elements
Common three-dimensional solid elements
C3D4
4-node linear tetrahedron
C3D6
6-node linear triangular prism
C3D8
8-node linear brick
C3D8R
8-node linear brick, reduced integration with hourglass control
C3D10
10-node

Chapter 5
Frame and Grid Equations
Introduction
This chapter develops the equations and methods for solution of plane frames and grids.
Develop the stiffness matrix for a beam element arbitrarily oriented in a plane.
Include the axial nodal displacement

Chapter 4
Development of Beam Equations
Introduction
Review basic concepts of beam bending.
Derive the stiffness matrix for the bending of a beam element. The beam element is
considered to be straight and to have constant cross-sectional area.
Illustra

Chapter 9 Axisymmetric Elements
Introduction
In this chapter, we consider a special two-dimensional element called the axisymmetric element.
This element is quite useful when symmetry with respect to geometry and loading exists about
an axis of the body b

Chapter 2
Introduction to Displacement (Stiffness) Method
Introduction
This chapter introduces some of the basic concepts on which the direct stiffness
method is founded. The linear spring is introduced first because it provides a
simple yet generally ins

A First Course in the
Finite Element Method
Introduction
The finite element method (FEM) is a numerical method for solving
problems of engineering and mathematical physics.
Typical problem areas include structural analysis, heat transfer, fluid
flow, mass