Local Stresses In Magnetoelectroelastic Solid With A Cavity

The aim of this thesis is to study the anti-plane deformation and investigate the local stresses for acircular/elliptical cavity in a magnetoelectroelastic solid under remotely uniform in-planeelectromagnetic and/or anti-plane mechanical loading. The analysis is made through taking theelectromagnetic field inside the cavity into account. The work consists of two parts:Part-1: It is assumed that the cavity is so smaller that; based on Saint Venant Principle, the plate canbe considered an infinite plane. In this case, Stroh formulism and Green’s functions are used toinvestigate the local stresses. We can derive explicit solutions in closed forms and then by reducingthe cavity into a crack, we can obtain the crack solution for electrically impermeable and permeablecrack. Numerical results are also presented to discuss behavior of local stresses and the study showsthat crack interior’s dielectric constants has effect on the distribution of mechanical stress, electric andmagnetic fields.Part-2: A finite plate is considered. Based on the extended Stroh formulism for a transversely isotropicmagneto-electro-elastic material under anti-plane deformation, the boundary collocation method(BCM) is used to study the2D problem of a finite plate with a circular/elliptic cavity. Laurent series isadopted to express the analytical function corresponding to the fields inside the circular cavity and inthe finite solid domain, whereas Faber series with conjunction of conformal transformation method isapplied to express the analytical function associated with the fields inside the elliptic cavity.Numerical algorithm is developed based on boundary collocation method to deal with the tractionboundary condition (i.e. Neumann BC) at the edges of the plate and exactly electric permeable,natural boundary condition (i.e. Dirichlet BC) at the cavity surface. Boundary Element Method andFinite Element Method are also presented by using the special Green function based on complexpotential theory and hybrid variation principle. Graphical results are presented to show the behaviorsof local stresses, both inside the cavity and around its surface. The solution shows that the electric andmagnetic fields inside the cavity are uniform in the case of finite plate, which is the same as the caseof an infinite plate. The aim of this thesis is to study the anti-plane deformation and investigate the local stresses fora circular/elliptical cavity in a magnetoelectroelastic solid under remotely uniform in-planeelectromagnetic and/or anti-plane mechanical loading. The analysis is made through taking theelectromagnetic field inside the cavity into account. The work consists of two parts:Part-1: It is assumed that the cavity is so smaller that; based on Saint Venant Principle, the plate canbe considered an infinite plane. In this case, Stroh formulism and Green’s functions are used toinvestigate the local stresses. We can derive explicit solutions in closed forms and then by reducingthe cavity into a crack, we can obtain the crack solution for electrically impermeable and permeablecrack. Numerical results are also presented to discuss behavior of local stresses and the study showsthat crack interior’s dielectric constants has effect on the distribution of mechanical stress, electric andmagnetic fields.Part-2: A finite plate is considered. Based on the extended Stroh formulism for a transversely isotropicmagneto-electro-elastic material under anti-plane deformation, the boundary collocation method(BCM) is used to study the2D problem of a finite plate with a circular/elliptic cavity. Laurent series isadopted to express the analytical function corresponding to the fields inside the circular cavity and inthe finite solid domain, whereas Faber series with conjunction of conformal transformation method isapplied to express the analytical function associated with the fields inside the elliptic cavity.Numerical algorithm is developed based on boundary collocation method to deal with the tractionboundary condition (i.e. Neumann BC) at the edges of the plate and exactly electric permeable,natural boundary condition (i.e. Dirichlet BC) at the cavity surface. Boundary Element Method andFinite Element Method are also presented by using the special Green function based on complexpotential theory and hybrid variation principle. Graphical results are presented to show the behaviorsof local stresses, both inside the cavity and around its surface. The solution shows that the electric andmagnetic fields inside the cavity are uniform in the case of finite plate, which is the same as the caseof an infinite plate.