Quasi-Generalized Virtual Work Principle and 3-Kind Variable of Generalized Variational Principle in Elastic Theory

Abstract

This paper presents a new method of forming generalised variational principle (GVP), i.e. primarily to assume that stress, strain and displacement are independent variables one another, and by method of weighted residuals, a principle of quasi-generalised virtual work equivalent to whole equations and boundary conditions in elastic theory is established, and then, further to derive two very comprehensively GYP involving three independent variables and known functions, Up-to-now, various 3-kind variable GYP could all be included in these two variational principles. And moreover, the Author further derives quasi-generalised virtual principle involving elastic boundary conditions, and two 3-kind variable GYP. These principles would be very useful as a theoretical tool in tackling to establishing methods of any non-coordinated finite elements in elastic theory.