Large-deformation analysis of a stepped laminated beam using a flexible constraint variational method

This paper presents a method for modelling large deflections of non-uniform multilayer beams. The method is based on a geometrically accurate model framework that accurately describes the units of the segments partitioned out of a non-uniform beam. It employs independent variables for the derivation of dis-placements and rotations of the centerline. A constrained variational approach is employed to introduce the geometrically varying non-linearities induced by large deflections into the control equations in their entirety. This approach can be used without modification of the admissible function, and the boundary conditions of the beam can be freely defined without modifying the admissible function. Furthermore, the hinge, clamped and free boundaries can be handled very flexibly by adjusting the boundary control parameters. Finally, the computational results of the present algorithm are compared with those obtained using the nonlinear finite element method, and the flexibility and accuracy of the proposed method are verified by a series of numerical examples. Furthermore, the large deformation of stepped double-layer beam structures is analyzed in depth, and the influences of the step positions, step lengths, step thicknesses, boundary conditions, and material properties on the frequency nonlinearities are explored. It is notable that specific geometrical parameters of the beam steps can eliminate the frequency nonlinearity.