Trefftz collocation method for two-dimensional strain gradient elasticity

Indirect Trefftz method is proposed for solving two-dimensional boundary value problems of the strain gradient elasticity theory (SGET). A system of trial functions satisfying the fourth-order equilibrium equations of SGET are developed based on the generalized Papkovich-Neuber potentials. The classical part of the displacement solution is represented through the T-complete system of functions satisfying the Laplace equation. The gradient part of the solution is represented through the system of heuristic functions satisfying the Helmholtz equation. The least squares collocation method is used to enforce the boundary conditions. Numerical examples are presented for the square domain under non-uniform tensile and bending loads. It is shown, that the advantage of the presented method is that it allows to directly control the accuracy of the fulfillment of all nonstandard boundary conditions, that are prescribed in SGET on the surfaces and edges of the body.

Automated summary

The indirect Trefftz method is proposed for solving two-dimensional boundary value problems of the strain gradient elasticity theory (SGET). A system of trial functions based on the generalized Papkovich-Neuber potentials is developed to satisfy the fourth-order equilibrium equations of SGET. The method allows direct control over the accuracy of fulfilling all nonstandard boundary conditions prescribed in SGET.