Abstract
This chapter discusses the approximate methods of analysis of bending of plates. These methods fall into two categories: (1) the first involves those that start from the governing differential equation whose approximate solution is obtained by numerical methods, and (2) the second involves those that are based on the principle of minimum potential energy or on allied energy principles. The strain energy of a deformed plate may be regarded as the sum of that because of bending and that because of stretching of the middle surface. The principle of minimum total potential energy can then be applied to obtain an approximate solution to plate problems. The chapter describes a form for the deflexion that satisfies the boundary conditions and that contains a number of disposable parameters. It also presents a linear combination of the form w = n=1∑N Bnwn (x,y) or, more generally, w = m = 1∑Mn=1∑NBmnwmn, where the parameters Bmn are determined from the MN equations.
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