Liu Yingxi

Formulation of Quasi-Conforming element and Hu-Washizu principle

Abstract A new, convenient and general method called Quasi-Conforming Element Technique is introduced for Finite Element Formulations in which the strain is discretized in terms of nodal values and then the potential energy is used to obtain stiffness matrix. The Quasi-Conforming Element Technique is a multivariate finite element method so that it includes the compatible, incompatible and hybrid stress model as its special cases. The connection between this technique and Hu-Washizu principle is shown.

Chaos-regularization hybrid algorithm for nonlinear two-dimensional inverse heat conduction problem

A numerical model of nonlinear two-dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature. Combining the chaos optimization algorithm with the gradient regularization method, a chaos-regularization hybrid algorithm was proposed to solve the established numerical model. The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regularization method to escape from local optima in the hybrid algorithm. Under the assumption of temperature-dependent thermal conductivity changing with temperature in linear rule, the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements. Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values, and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.

A triangular quasi-conforming finite element for transient dynamic analysis

A type of 3 node triangular element is constructed by the Quasi-conforming method, which may be used to solve the equation of a type of inverse problem of wave propagation after Laplace transformation Δu−A2u=0. The strains in the element are approximated by an exponential function and the string-net function between neighbouring elements is approximated by one dimensional general solution of the equation. Furthermore the strain field satisfies the equation, and therefore in the derivation of the element formulation, no shape function is needed. In this sense, it is a kind of hybrid element. Compared with the ordinary linear triangular element, the new one features higher precision with coarse meshes. Some numerical tests are presented.