The Bending Problem Of Magnetoelectroelastic Plates Based On The Strain Gradient Theory

Based on the strain gradient theory,the bending problem of magnetoelectroelastic single-layered plate and piezoelectric-piezomagnetic bi-layered plates are studied.A meshless method based on polynomial particular solutions is used to solve the governing equations and boundary conditions.The meshless method based on polynomial particular solution is introduced in detail to solve linear partial differential equations with constant coefficients.The effects of bending properties of magnetoelectroelastic single-layered plate and piezoelectric-piezomagnetic bi-layered plates are also discussed.The main research contents are as follows:Based on the strain gradient theory,using the Hamilton variational principle,the governing equations and boundary conditions of magnetoelectroelastic single-layered plate are deduced in detail.The governing equations and boundary conditions are solved by the polynomial particular solution method,and the influence of the calculation parameters of the polynomial particular solution method on the calculation results is discussed,which further verifies the superiority of the polynomial particular solution method.The influences of the strain gradient theory,Pasternak foundation parameters,applied electric and magnetic potentials,length-width ratio,mechanical load and boundary conditions on the maximum value of deflection and absolute values of rotations in magnetoelectroelasric single-layered plate are given in detail.Considering layerwise theory,the governing equations and boundary conditions of the piezoelectric-piezomagnetic bi-layered plates based on the strain gradient theory are derived in combination with the Hamilton variational principle,and the polynomial particular solution method is used to solve them.The influences of the strain gradient theory,Pasternak foundation parameters,boundary conditions,piezoelectric layer thickness,length-width ratio,loading types and on the maximum values of deflection,electric potential and magnetic potential in piezoelectric-piezomagnetic bi-layered plates are discussed in detail.