Evaluation of Stress Distribution of Isotropic, Composite, and FG Beams with Different Geometries in Nonlinear Regime via Carrera-Unified Formulation and Lagrange Polynomial Expansions

Abstract

In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in the cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme and an arc length method are used in the solution of nonlinear equations by finite element method to determine the mechanical effect. The Carrera-Unified formulation (CUF) is used to solve nonlinear, low or high order kinematic refined structure theories for finite beam elements. In the study, displacement area and stress distributions of composite structures with different angles and functionally graded (FG) structures are presented for Lagrange polynomial expansions. The results show the accuracy and computational efficiency of the method used and give confidence for new research.

Elastic buckling of a generalized cylindrical sandwich panel under axial compression

“…This generalization concerning the continuity of symmetrical variation of mechanical properties in the thickness direction of the structures and the individual nonlinear function of deformation of the straight normal line to the neutral surface. Carrera et al [22] investigated the nonlinear displacement and stress distributions in the crosssection effect of the isotropic beam, composite beam placed at different angles, and FG beams by CUF theory. Wu et al [23] developed an unified formulation of full geometrically nonlinear refined shell theory based on the CUF and the total Lagrangian approach to predict the post-buckling, largedeflection, snap-through and snap-back nonlinear responses with high accuracy.…”

Multiple Time-Scales Analysis to Predict the Quasiperiodic Oscillatory Response of a Thin-Walled Beam Subjected to 1 : 1 : 1 Simultaneous Resonance

“…Tey illustrated the practical capability of thin-walled beams by fuid-structural interaction simulation of a hydrokinetic blade subjected to a feld condition. Carrera et al [42] used Lagrange polynomials in order to study the nonlinear behavior resulting from large displacements and rotations in a thin-walled composite beam under axial loading and diferent angles of the composite structures. Te proposed Carrera unifed formulation provided accurate results in investigating the nonlinear behavior of composite, isotropic, and FG beams with axial loading.…”