Nonlinear Structural Engineering


Basic Theories and Principles of Nonlinear

Beam Deformations






1.1 Introduction

The minimum weight criteria in the design of aircraft and aerospace vehicles,

coupled with the ever growing use of light polymer materials that can undergo

large displacements without exceeding their specified elastic limit, prompted

a renewed interest in the analysis of flexible structures that are subjected

to static and dynamic loads. Due to the geometry of their deformation, the

behavior of such structures is highly nonlinear and the solution of such problems

becomes very complex. The solution complexity becomes immense when

flexible structural components have variable cross-sectional dimensions along

their length. Such members are often used to improve strength, weight and

deformation requirements, and in some cases, architects and planners are using

variable cross-section members to improve the architectural aesthetics and

design of the structure.

In this chapter, the well known theory of elastica is discussed, as well as

the methods that are used for the solution of the elastica. In addition, the solution

of flexible members of uniform and variable cross-section is developed

in detail. This solution utilizes equivalent pseudolinear systems of constant

cross-section, as well as equivalent simplified nonlinear systems of constant

cross-section. This approach simplifies a great deal the solution of such complex

problems. See, for example, Fertis [2, 3, 5, 6], Fertis and Afonta [1], and

Fertis and Lee [4].

This chapter also includes, in a brief manner, important historical developments

on the subject and the most commonly used methods for the static

and the dynamic analysis of flexible members.



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