Abstract
The geometrical nonlinear effects caused by large displacements and rotations over the cross section of composite thin-walled structures are investigated in this work. The geometrical nonlinear equations are solved within the finite element method framework, adopting the Newton–Raphson scheme and an arc-length method. Inherently, to investigate cross-sectional nonlinear kinematics, low- to higher-order theories are employed by using the Carrera unified formulation, which provides a tool to generate refined theories of structures in a systematic manner. In particular, beams and shell-like laminated composite structures are analyzed using a layerwise approach, according to which each layer has its own independent kinematics. Different stacking sequences are analyzed, to highlight the influence of the cross-ply angle on the static responses. The results show that the geometrical nonlinear effects play a crucial role, mainly when higher-order theories are utilized.
Highlights
Composite materials have encountered great success during recent decades
Kapania and Raciti [6] worked in the framework of the nonlinear finite element method (FEM), which is the main focus of the proposed research
This paper is organized as follows: (i) first, the formulation of the adopted refined beam theory is presented in Sect. 2; (ii) subsequently, Sect. 3 introduces the geometrical relations and the constitutive expressions for composite materials; (iii) Sect. 4 describes the derivation of the nonlinear governing relations and the fundamental nuclei (FN) of secant and tangent matrices for the solution of the geometrical nonlinear problem; (iv) different loading and structural cases are considered as numerical results in Sect. 5; (v) the main conclusions are given
Summary
Composite materials have encountered great success during recent decades. Their usage on sophisticated structural components has drastically grown in many engineering fields, such as automotive and aerospace, among the others. Section, the first-order shear deformation theory (FSDT) has been developed This model has been adopted by engineers for their study on the analysis of laminated structures. Kapania and Raciti [6] worked in the framework of the nonlinear finite element method (FEM), which is the main focus of the proposed research They developed a simple 1D model for the nonlinear analysis of symmetrically and asymmetrically laminated composite beams, including shear deformation, bending–stretching coupling, and twisting. The problem we address in this work is if the nonlinear kinematic equations are strictly mandatory even if an higher-order model is adopted for the structural analysis and which level of accuracy is reached, considering various cross section shapes, from compact to thin-walled ones. This paper is organized as follows: (i) first, the formulation of the adopted refined beam theory is presented in Sect. 2; (ii) subsequently, Sect. 3 introduces the geometrical relations and the constitutive expressions for composite materials; (iii) Sect. 4 describes the derivation of the nonlinear governing relations and the FNs of secant and tangent matrices for the solution of the geometrical nonlinear problem; (iv) different loading and structural cases are considered as numerical results in Sect. 5; (v) the main conclusions are given
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