Finite element analysis is a computer-based numerical method for solving engineering problems in bodies of user-defined geometry. This article introduces the important issues of finite elements (especially accuracy and efficiency) in a nonacademic manner. It describes the Rayleigh-Ritz procedure for solving structural problems based on the principle of virtual work. The article discusses continuum elements, such as hexahedra, pentahedra, tetrahedra, quadrilaterals, and triangles, commonly used in three- or two-dimensional domains. It considers structural elements such as beam element, plate element, shell element, and elbow element. The article presents three examples to illustrate the types of problems that can be addressed and the decisions that must be made when using finite element analysis.

This article provides an overview of the finite-element-based analyses (FEA) of advanced composite structures and highlights key aspects such as the homogenization of materials properties and post-processing of numerical results. It discusses the analysis of composite structures based on micromechanics and macromechanics. The article describes the FEA of 3-D solid elements, 2-D cylindrical shell elements, and 1-D beam elements. It contains a table that lists the commercially available finite element codes related to the analysis of fibrous composite materials. The article presents classical examples of the mechanics of composite materials to illustrate the aspects of multilayered composite structures.

This article provides information on the development of finite element analysis (FEA) and describes the general-purpose applications of FEA software programs in structural and thermal, static and transient, and linear and nonlinear analyses. It discusses special-purpose finite element applications in piping and pressure vessel analysis, impact analysis, and microelectronics. The article describes the steps involved in the design process using the FEA. It concludes with two case histories that involve the use of FEA in failure analysis.

When complex designs, transient loadings, and nonlinear material behavior must be evaluated, computer-based techniques are used. This is where the finite-element analysis (FEA) is most applicable and provides considerable assistance in design analysis as well as failure analysis. This article provides a general view on the applicability of finite-element modeling in conducting analyses of failed components. It highlights the uses of finite-element modeling in the area of failure analysis and design, with emphasis on structural analysis. The discussion covers the general development and both general- and special-purpose applications of FEA. The special-purpose applications of FEA covered are piping and pressure vessel analysis, impact analysis, and microelectronic and microelectromechanical systems analysis. The article provides case histories that involved the use of FEA in failure analysis.