Nonlinear mathematical modeling of the thermo-magneto-electro-elastic behavior of an anisotropic plate of complex shape
Keywords:
R-functions method, plate of complex shape, anisotropic composite material, von Kármán nonlinearity, thermo-magneto-elasticity, Lorentz force, Duhamel–Neumann law, Bubnov–Galerkin method, Newmark schemeAbstract
The paper proposes a mathematical model describing the nonlinear deformation of anisotropic plates of complex shape under the action of thermo-magneto-electro-elastic fields, together with a computational algorithm for its solution. The model is based on a first-order kinematic (shear deformation) theory that accounts for transverse shear, and on von Kármán geometric nonlinearity describing large deflections; the coupled effect of the temperature, electric and magnetic fields on the anisotropic medium is introduced into the constitutive equations through the Duhamel–Neumann law and Maxwell's equations. An arbitrary multiply connected plate domain and mixed boundary conditions are described by a single analytical expression using the R-functions method, and a solution structure that exactly satisfies the boundary conditions is constructed. Spatial discretization is performed by the Bubnov–Galerkin method with Gaussian quadratures, while time integration is carried out using the implicit Newmark scheme and an iterative algorithm based on an equivalent stiffness matrix for the nonlinear terms
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