Parametrized Lagrange multiplier method and construction of generalized mixed variational principles for computational mechanics Original Research Article

This paper provides a general means, called the parametrized Lagrange multiplier method (PLM), for constructing new variational principles from any existing one. PLM is more powerful than the traditional Lagrange multiplier (TLM) in many aspects; it can explain many theoretical problems and do plenty, which have been troublesome before. In mathematics, PLM could be considered as an approach to solve a subset of the inverse problem of variational calculus. In elasticity, the variational principle constructed by PLM is called the generalized mixed variational principle (GMVP), featuring some parameter-functions called the splitting factors and playing an important role in overcoming the ill-conditioned problems in finite element analysis. This paper introduces PLM and GMVP, while their applications such as how to deal with the ill-conditioned problems by means of GMVP will be discussed some time later in other papers.