The Finite Element Method
The Finite Element Method
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DOI：
10.1007/978-3-030-04348-3_5
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
A. Shabana
中科院分区：
文献类型：
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作者：
A. Shabana
在上一章末尾提出的求解连续系统振动问题的近似方法是基于这样的假设：连续系统的变形形状可以用一组假定函数来描述。利用这种方法，具有无限多个自由度的连续系统的振动可以用有限个常微分方程组来描述。然而，这种方法可以用于具有简单几何形状的结构元素的情况，如杆、梁和板。在具有复杂几何形状的大系统中，在定义假定的形状函数时可能会遇到困难。为了克服这些问题，有限元方法被广泛应用于大型结构系统的动力分析中。有限元方法是一种数值方法，可用于获得一大类工程问题的近似解。特别是，有限元方法非常适合于具有复杂几何形状的问题。
The approximate methods presented at the end of the preceding chapter for the solution of the vibration problems of continuous systems are based on the assumption that the shape of the deformation of the continuous system can be described by a set of assumed functions. By using this approach, the vibration of the continuous system which has an infinite number of degrees of freedom is described by a finite number of ordinary differential equations. This approach, however, can be used in the case of structural elements with simple geometrical shapes such as rods, beams, and plates. In large-scale systems with complex geometrical shapes, difficulties may be encountered in defining the assumed shape functions. In order to overcome these problems, the finite element (FE) method has been widely used in the dynamic analysis of large-scale structural systems. The FE method is a numerical approach that can be used to obtain approximate solutions to a large class of engineering problems. In particular, the FE method is well suited for problems with complex geometries.