Precise semi-analytical solutions for the static analysis of laminated arch beams in elevation with deep curvature

This article presents a two-dimensional (2D) semi-analytical formulation for the static analysis of laminated arch beams with various boundary conditions. The proposed model is based on the general elasticity theory of 2D curved beams; thus, the derived governing equations satisfy the interlaminar continuity of displacements and stresses and stress boundary conditions on the top and bottom beam’s surfaces. Navier-type closed-form solutions and the differential quadrature method (DQM) are used to solve the governing equations for simply supported arch beams. The two-dimensional form of DQM is employed to solve the governing equations for clamped-clamped and clamped-free boundary conditions. The proposed solutions are validated against results reported in the literature and commercial software finite elements for isotropic and laminated arch beams with different boundary conditions. A simplified model based on the theory of shallow curved beams is discussed for simply supported laminated arch beams. This investigation highlights the extent of the proposed formulation for laminated arch beams with different material configurations, geometric properties, and boundary conditions, thus providing valuable results for validating simplified curved beam theories and finite element solutions.