Proposal,development and applications of parametric variational principle
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.
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