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Twierdzenie wariacyjne gradientowej termodyfuzji lepkosprężystej

Kubik J.

Roczniki Inżynierii Budowlanej

2014

z. 14

41--44

The variational theorem is derived for the boundary problems of gradient thermomechanics. Heat and mass flows coupled with a mechanical problem are analysed in the work within a framework of the gradient theory.

A parametrized variational principle of nonlinear piezoelectricity

He J-H.

Computer Assisted Mechanics and Engineering Sciences

2003

Vol. 10, No. 3

263-269

The variational theory is the theoretical basis of the finite element method, meshfree particle methods and other modern numerical techniques. The present paper establishes a family of variational principles for nonlinear piezoelectricity. A new constitutive relation is suggested, which is deduced as a stationary condition of a generalized variational principle. Keywords: variational theory, piezoelectricity, constitutive equations.

Variational principles of bending problems of thin plates

He Ji-Huan

Archives of Mechanics

2001

Vol. 53, nr 6

631-642

In this paper, via the semi-inverse method proposed previously by the present author, a family of variational principles of bending problems of plates is derived directly from their governing equations and boundary conditions, without using the Lagrange multiplier method. In this method, an energy-like trial functional is constructed with a certain unknown function, which can be identified step by step. A new generalized variational principle is obtained.