参变量变分原理的提出、发展与应用

Proposal,development and applications of parametric variational principle

参变量变分原理及其参数二次规划算法是由钟万勰院士1985年针对弹性接触边界非线性问题首次提出来的,经过将近40年的不断发展,目前参变量变分原理已经成功应用于各个领域,其中包括弹塑性分析、接触问题、润滑力学、岩土力学、变刚度杆系结构、先进材料性能分析、材料的蠕变与损伤、柔性结构力学和LQ最优控制等各个工程领域.本文首先回顾了参变量变分原理的起源,介绍了参变量变分原理的基本概念,然后以弹塑性分析问题为例,阐明建立参变量变分原理的理论模型以及实现数值参数二次规划求解原理,最后详细回顾了参变量变分原理的基本理论与相应数值算法在各个领域的发展及其工程应用,展示了参变量变分原理在求解各类非线性问题的特色与优势.

The parametric variational principle and its parametric quadratic programming algorithm were first proposed by Academician ZHONG Wanxian in 1985 for the nonlinear boundary problem of elastic contact.After nearly 40 years of continuous development,the parametric variational principle has been successfully applied to various fields,including elastoplastic analysis,contact,mechanics lubrication mechanics,geotechnical mechanics,variable stiffness rod structure,advanced material performance analysis,creep and damage of materials,flexible structural mechanics,LQ optimal control and other engineering fields.This paper first reviews the origin of the parametric variational principle,introduces the basic concepts of parametric variational principle,then takes an elastoplastic analysis problem as an example to clarify how to establish the theoretical model of the parametric variational principle and realize its quadratic programming solution,and finally reviews in detail the basic theory of the parametric variational principle and the development and engineering application of corresponding numerical algorithms in various fields,showing the characteristics and advantages of the parametric variational principle in solving various nonlinear problems.