Variational Principles And Simple Applications Of Magnetoelectroelasticity And Thermal Magnetoelectroelasticity

Magnetoelectroelasticity is a kind of special composite materials that can achieve transformation among mechanical energy, electric energy and magnetic energy. Thermal magnetoelectroelasticity is a kind of special composite materials that can achieve transformation among mechanical energy, electric energy, magnetic energy, and heat energy. They have shown good prospects in information technology, non-destructive testing, new material technology, new intelligent materials and structures, and many other high-tech fields, and are becoming hotspot topic of the mechanics, strength of materials and physics.Variational method is a kind of effective approximate calculation method that can be used to (thermal) magnetoelectroelasticity. The prominent advantage of variational method is that it can adopt simple trial-functional to simulate the coupled problem of fields, and get near-precise solution without solving the field problem itself. The different types of functional, which we get from variational principles, provide a theoretical basis for FEM (Finite Element Method) of magnetoelectroelasticity.Base on the above two factors, this thesis aims at proving a family of variational principles of static magnetoelectroelasticity and static thermal magnetoelectroelasticity, then primarily studies the applications of the static magnetoelectroelastic variational principles.Firstly, this thesis resolves the variational principles of magnetoeletroelasticity of static system. It deduces the classical variational principle including the minimum total potential energy principle and the minimum complementary energy principle. Then it establishes the generalized varitional principles of magnetoelectroelasticity, which include the potential energy form and the complementary energy form variational principles of six kinds and nine kinds variable by bringing in Lagrange multiplayer. In addition, this thesis adopts Bianji method to solve the inverse problem of magnetoelectroelasticity.Secondly, this thesis studies variational principles of the thermal magnetoelectro- elasticity and establishes various variational principles of it on the basis of generalized virtual work theory of the thermal magnetoelectroelasticity. It also includes the classical and generalized variational principles. The classical variational principle includes the potential energy principle and the complementary energy principle. The generalized varational principles include the potential energy form and the complementary energy form variational principles of seven kinds and ten kinds variable by bringing in Lagrange multiplayer.Finally, this thesis investigates the applications of magnetoelectroelasticity preliminarily. On the basis of the minimum total potential energy principle of magneto- electroelasticiy it deduces the balance equations and boundary conditions of magneto- electroelastic bar and magnetoelectroelastic plane beam, which are common structures in project.