Internal force and displacement prediction system and method for variable cross-section axial functionally gradient beam

The invention provides an internal force and displacement prediction system and method for a variable-cross-section axial functional gradient beam, and relates to the technical field of building structure calculation and analysis, the internal force and displacement of a nonlinear variable-cross-section axial functional gradient Timoshenko beam on a Pasternak foundation can be calculated, and the method comprises the following steps: obtaining a total energy equation of a constant-cross-section uniform Timoshenko beam on the Pasternak foundation through an energy method; an equilibrium differential equation of the Timoshenko beam is obtained through a variational method; a deflection control equation of the Timoshenko beam is obtained; based on a deflection control equation of the Timoshenko beam, a general solution of a fourth-order differential equation is obtained, and an expression of deflection is obtained; a matrix form is obtained by using an initial parameter method, and the variable cross-section fun