Rational nonlinear analysis of framed structures and curved beams considering joint equilibrium in deformed state
TL;DR: In this paper, a rigorous formulation for the linearized stiffness equation of three-dimensional beam elements with account taken of the joint moment equilibrium in the deformed configuration C 2 is presented.
Abstract: Based on the continuum mechanics principles, a rigorous formulation is presented for the linearized stiffness equation of three-dimensional beam elements with account taken of the joint moment equilibrium in the deformed configuration C 2 By sticking to the Bernoulli–Euler hypothesis of plane sections and elasticity definitions for stress resultants, the bending moments and torque of the element are shown to be quasi- and semi-tangential, respectively, in the updated Lagrangian formulation Further, by invoking the moment equilibrium conditions for structural nodes at C 2 , the induced moment matrix that first appears to be antisymmetric on the element level turns out to be symmetric upon assembly of all elements on the structural level The joint equilibrium conditions at C 2 , as represented by the induced moment matrix, are central not only to the out-of-plane buckling analysis of angled frames, but also to the simulation of curved beams by the straight-beam elements Examples on the buckling of angled frames and curved beams are provided to support the theory presented
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TL;DR: In this article, an invariant isogeometric formulation for the geometric stiffness matrix of spatial curved Kirchhoff rods considering various end moments, i.e., the internal (member) moments and applied (conservative) moments, is presented.
8 citations
01 Apr 2022
TL;DR: In this paper , the buckling of single beams and two-and three-member frames subjected to torques at the supports is analyzed for a solid rectangular cross-section, and different aspect ratios are analyzed to investigate the effect of changing the ratio between the minor and major second moments of area on the bucking torque and associated buckling mode.
Abstract: The paper presents analytical solutions for the buckling of single beams as well as two- and three-member frames subjected to torques at the supports. The governing equations and their solutions are stated, including boundary conditions and continuity conditions at connections between members, and buckling solutions are provided for a wide range of support conditions and frame geometries. The cross-section is assumed to be solid or hollow and accordingly, warping effects are ignored. The presented solutions are for a solid rectangular cross-section, and different aspect ratios are analysed to investigate the effect of changing the ratio between the minor and major second moments of area on the buckling torque and associated buckling mode. Solutions are provided for both the critical mode and higher-order modes, allowing mode-changes between symmetric and asymmetric modes to be identified.
3 citations
Journal Article•
TL;DR: In this paper, a finite element formulation for the large deformation analysis of space-frame structures is presented, which is based on second-order geometric nonlinear theory and Vlasov's theory for thin-walled beams.
Abstract: A finite element formulation for the large‐deformation analysis of space‐frame structures is presented. The formulation is based on second‐order geometric nonlinear theory and Vlasov's theory for thin‐walled beams (i.e., large displacement of members with small strains, which includes the warping deformation influence). The influence of member‐distributed loading on the geometric nonlinear response of space‐frame structures also is included. An updated Lagrangian formulation is used to model large joint translations and rotations. Prismatic beams of arbitrary cross section are considered. Rodriguez's modified rotation vector is used to represent angular deformations, which avoids rotational discontinuities at the joints of deformed space‐frame structures. Numerical results and algorithmic details are presented in a companion paper.
2 citations
TL;DR: In this article, the critical issue of thin-walled beams with laterally fixed ends was studied and the method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated.
Abstract: This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. ...
1 citations
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01 Jan 1969
TL;DR: In this article, the authors propose a linearized theory of elasticity for tensors, which they call Linearized Theory of Elasticity (LTHE), which is based on tensors and elasticity.
Abstract: 1. Vectors and Tensors. 2. Strain and Deformation. 3. General Principles. 4. Constitutive Equations. 5. Fluid Mechanics. 6. Linearized Theory of Elasticity. Appendix I: Tensors. Appendix II: Orthogonal Curvilinear.
3,658 citations
TL;DR: In this paper, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived starting from continuum mechanics principles, and a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure.
Abstract: SUMMARY Starting from continuum mechanics principles, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived. The aim in this paper is a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure. The general formulations include large displacements, large strains and material non-linearities. For specific static and dynamic analyses in this paper, elastic, hyperelastic (rubber-like) and hypoelastic elastic-plastic materials are considered. The numerical solution of the continuum mechanics equations is achieved using isoparametric finite element discretization. The specific matrices which need be calculated in the formulations are presented and discussed. To demonstrate the applicability and the important differences in the formulations, the solution of static and dynamic problems involving large displacements and large strains are presented.
789 citations
TL;DR: In this article, an updated Lagrangian and a total Lagrangians formulation of a three-dimensional beam element are presented for large displacement and large rotation analysis, and it is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors.
Abstract: An updated Lagrangian and a total Lagrangian formulation of a three-dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are given.
633 citations