We investigate thin plates where out-of-plane deformations arise due to membrane kinematic incompatibility of rotational type, specifically Volterra wedge disclinations, which are commonly observed in metal plates and graphene. We present theorems that guarantee the existence and regularity of equilibrium solutions in the presence of a finite number of disclinations and a dead load, for clamped plates. To solve the equilibrium equations, we implement a numerical code in the FEniCS environment and apply it to a series of parametric test studies. Our Finite Element method follows the Discontinuous Galerkin approach with C0 elements.

翻译：本研究探讨了由旋转型膜面运动学不相容（特别是Volterra楔形向错）引起面外变形的薄板，此类现象常见于金属板和石墨烯中。针对含有限个向错和固定载荷的夹支板，我们提出了保证平衡解存在性与正则性的定理。为求解平衡方程，我们在FEniCS环境中开发了数值计算程序，并将其应用于系列参数化测试研究。采用的有限元方法遵循基于C0单元的间断Galerkin法。