Transient deformation of an anisotropic plate during individual modeling of local supports along an arbitrary contour

A mathematical formulation of a transient problem for an anisotropic plate on an elastic inertial foundation is given. An original method for solving it has been developed and implemented. The plate has local fixings of various nature located along its boundary. The plate boundary can have an arbitrary shape. A fundamental solution for an unbounded anisotropic plate is found and used in order to construct resolving integral representations. This solution is obtained using the Fourier integral transform in spatial coordinates domain and the Laplace integral transform in time domain. The corresponding original is constructed using analytic inverse method for the Laplace integral transform. The original of the two-dimensional Fourier transform is found numerically using integration methods for rapidly oscillating functions. A special algorithm allowing to obtain the originals of the two-dimensional Fourier transform numerically with a required accuracy is designed and implemented. Using the fundamental solution and the method of compensating loads the integral representations for transient displacements, moments and angles of rotation of plate sections are obtained. The time-dependent compensating loads are derived from the solution of a system of Volterra equations of the first kind. This system is solved step by step in time. At each time step, the problem is reduced to an equivalent system of algebraic equations. The results are compared with the solution obtained using the finite element method. The convergence of the proposed method was evaluated. Graphical results of calculations are given.