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.

中文翻译：

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二维应变梯度弹性的Trefftz配置方法

提出了间接Trefftz方法来解决应变梯度弹性理论（SGET）的二维边值问题。基于广义Papkovich-Neuber势，开发了一个满足SGET四阶平衡方程的试验函数系统。位移解的经典部分由满足Laplace方程的T-完全函数系统表示。解的梯度部分通过满足Helmholtz方程的启发式函数系统表示。最小二乘配置方法用于强制执行边界条件。给出了在非均匀拉伸和弯曲载荷下平方域的数值示例。如图所示，