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(一) 结构与介质分析是力学学科中极为主要的一个方面。这一古老学科经近百年来的发展已经成、为各自然科学中在数学上较为完整、严密和系统的一门科学,至今基本理论已相当成熟。但由于数学方法上的困难,许多问题特别是一些高维问题能得到精确解析解的范围还是有限的。但是近二、三十年来计算技术发展,特别是有限元法的提出与应用已使结构与介质分析问题的求解达到一个飞跃。目前只要确立基本方程,原则上任何这方面问题都能用有限元法来加以求解。有限元法之所以得到如此迅速发展和被广泛应用,一方面是其解决问题的能力高,另一方面也在于便于掌握。因为用有限元法解决实际问题,只需有关人员了解问题的基本关系式和共同的计算技术,而不需要一般技术人员难于掌握的比较复杂的应用数学知识。有限元法发展到现在(虽然时间不长),已经渗透到力学及其它自然科学各个领域中。但随着应用的广泛深入,有些问题也越
(a) Structural and media analysis is an extremely important aspect of the discipline of mechanics. The development of this ancient discipline over the past century has become a science that is mathematically complete, rigorous, and systematic in all natural sciences. The basic theory has been quite mature so far. However, due to the difficulties of mathematical methods, many problems, especially the scope of some high-dimensional problems that can get accurate analytical solutions, are still limited. However, the development of computational technology in the last two or three decades, especially the introduction and application of the finite element method has led to a leap forward in the solution of structural and media analysis problems. At present, as long as the basic equations are established, in principle any of these problems can be solved by the finite element method. The reason why the finite element method has been developed so rapidly and widely used is that on the one hand, it has a high ability to solve problems, and on the other hand it is easy to grasp. Because using the finite element method to solve practical problems, only the relevant personnel understand the basic relationship of the problem and the common computing technology, rather than the more complex applied mathematics knowledge that is difficult for general technicians to grasp. The development of the finite element method to the present (although not too long) has penetrated into the fields of mechanics and other natural sciences. However, with the wide application of the application, some problems have become more serious.