Exercises

Method Joints Pin Jointed Truss

This Chapter begins the exposition of the Direct Stiffness Method DSM of structural analysis. The DSM is by far the most common implementation of the Finite Element Method FEM . In particular, all major commercial FEM codes are based on the DSM. The exposition is done by following the DSM steps applied to a simple plane truss structure. 2.1. WHY A PLANE TRUSS The simplest structural finite element is the bar also called linear spring element, which is illustrated in Figure 2.1 a . Perhaps the...

Finite Element Method With Maple

Computer algebra systems, known by the acronym CAS, are programs designed to perform symbolic and numeric manipulations following the rules of mathematics.1 The development of such programs began in the mid 1960s. The first comprehensive system the granddaddy of them all, called Macsyma an acronym for Project Mac Symbolic Manipulator was developed using the programming language Lisp at MIT's famous Artificial Intelligence Laboratory over the period 1967 to 1980. The number and quality of...

Distributed Force On Nodes Finite Element

In many thin structures modeled as continuous bodies the appearance of skinny elements is inevitable on account of computational economy reasons. An example is provided by the three-dimensional modeling of layered composites in aerospace and mechanical engineering problems. A physical interface, resulting from example from a change in material, should also be an interelement boundary. That is, elements must not cross interfaces. See Figure 8.3. In two-dimensional FE modeling, if you have a...