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一、有限单元法的基本原理为了便于分析问题,我们首先看一引例。图2—6(α)所示为一仅受自重作用的等截面直杆,杆长为 L,截面积 F,单位杆长重量为 q,弹性模量 E。试求杆内的应力。这个问题在“材料力学”中已有精确解答,它首先求出杆件的位移函数 u=u(x),如图2—6(c)中的二次曲线所示,再按几何方程与物理方程求出ε_x 和σ_x,公式如下:
First, the basic principle of the finite element method In order to facilitate the analysis of the problem, we first look at an example. Figure 2-6 (α) shows a straight rod with constant cross section only under self-weight. The rod length is L, the cross-sectional area is F, and the rod weight is q and modulus of elasticity. Try to find the stress in the rod. This problem has been accurately solved in “Mechanics of Materials”. It first finds the displacement function u = u (x) of the rod, as shown by the quadratic curve in Figure 2-6 (c) Physical equations to find ε_x and σ_x, the formula is as follows: