Topic
Tangent stiffness matrix
About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.
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TL;DR: In this paper, an integrated stiffness model is established for a Planar Parallel Manipulator (PPM) with actuation redundancy based on Finite Element Method (FEM), and the static stiffness, dynamitic stiffness, and moving stiffness of the PPM are analyzed according to the integrated model.
Abstract: An integrated stiffness model is established for a Planar Parallel Manipulator (PPM) with actuation redundancy based on Finite Element Method (FEM), and the static stiffness, dynamitic stiffness and moving stiffness of the PPM are analyzed according to the integrated stiffness model. Firstly, a dynamic model of flexible plane beam element is created as a basic unit for branches. Secondly, each branch is assembled in generalized coordinates, and the integrated stiffness model of the PPM is established. Then calculation and simulation for the static stiffness, dynamitic stiffness and moving stiffness are carried out. The results show that the static stiffness and dynamitic stiffness are related with the position and posture of the PPM. The moving stiffness shows that the elastic deformations cause the oscillation of the PPM. In this paper, three stiffness models are unified in the integrated stiffness model, which improves the efficiency of the stiffness calculation and mechanism design.
4 citations
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TL;DR: In this paper, a two-node spatial catenary cable element with arbitrary rigid arms is developed to determine the cable sag effect and solve the rigid connection problem at cable ends of a long-span cable-stayed bridge.
Abstract: To determine the cable sag effect and solve the rigid connection problem at cable ends of a long-span cable-stayed bridge, a two-node spatial catenary cable element with arbitrary rigid arms is developed. Using the finite rotation formula of the space vector and a differential method, the incremental relation between displacement and force at both ends of the rigid arm is given. Then, explicit expression of the tangent stiffness matrix of the element with arbitrary rigid arms is derived based on the catenary equations. Two numerical examples are provided to verify the validity of the new element. A long-span cable-stayed bridge application model is established, and the cables are simulated using three methods. The results show that the rigid end effect has influence on displacements, bending moments and rigidity and should not be ignored. The catenary cable element with arbitrary rigid arms can be used to simulate the geometric nonlinear mechanical behavior of the cables and can well solve the rigid connection problem.
4 citations
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TL;DR: In this article, a one-dimensional fiber beam element model was proposed to take account of materially non-linear behavior, benefiting the highly efficient elastic-plastic analysis of girders with shear-lag effects.
Abstract: This paper proposes a one-dimensional fiber beam element model taking account of materially non-linear behavior, benefiting the highly efficient elastic-plastic analysis of girders with shear-lag effects. Based on the displacement-based fiber beam-column element, two additional degrees of freedom (DOFs) are added into the proposed model to consider the shear-lag warping deformations of the slabs. The new finite element (FE) formulations of the tangent stiffness matrix and resisting force vector are deduced with the variational principle of the minimum potential energy. Then the proposed element is implemented in the OpenSees computational framework as a newly developed element, and the full Newton iteration method is adopted for an iterative solution. The typical materially non-linear behaviors, including the cracking and crushing of concrete, as well as the plasticity of the reinforcement and steel girder, are all considered in the model. The proposed model is applied to several test cases under elastic or plastic loading states and compared with the solutions of theoretical models, tests, and shell/solid refined FE models. The results of these comparisons indicate the accuracy and applicability of the proposed model for the analysis of both concrete box girders and steel-concrete composite girders, under either elastic or plastic states.
4 citations
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TL;DR: In this article, an equation for the effective tangent moduli for steel axial members of hot-rolled I-shaped section subjected to various residual stress distributions was presented. And the presented equations are extremely effective for accurately analyzing elastoplastic behavior of the axially loaded members in a simple manner without using complex shell element models.
Abstract: This paper presents an equation for the effective tangent moduli for steel axial members of hot-rolled I-shaped section subjected to various residual stress distributions. Because of the existence of residual stresses, the cross section yields gradually even when the member is subjected to uniform axial stresses. In the elasto-plastic stage, the structural response can be easily traced using rational tangent modulus of the member. In this study, the equations for rational tangent moduli for hot-rolled I-shaped steel members in the elasto-plastic stage were derived based on the general principle of force-equilibrium. For practical purpose, the equations for the tangent modulus were presented for conventional patterns of the residual stress distribution of hot-rolled I-shaped steel members. Through a series of material nonlinear analyses for steel axial members modeled by shell elements, the derived equations were numerically verified, and the presented equations were compared with the CRC tangent modulus equation, the most frequently used equation so far. The comparative study shows that the presented equations are extremely effective for accurately analyzing elasto-plastic behavior of the axially loaded members in a simple manner without using complex shell element models.
4 citations
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16 Jul 2015TL;DR: In this article, a phenomenological intralaminar plasticity model is proposed to represent the nonlinearity of fiber-reinforced polymer composite materials, and a four-parameter hardening model is built to capture important features of the hardening curve and consequently gives the good matching of the experiments.
Abstract: The nonlinearity of fibre-reinforced polymer (FRP) composites have significant effects on the analysis of composite structures. This article proposes a phenomenological intralaminar plasticity model to represent the nonlinearity of FRP composite materials. Based on the model presented by Ladeveze et al., the plastic potential and hardening functions are improved to give a more rational description of phenomenological nonlinearity behavior. A four-parameter hardening model is built to capture important features of the hardening curve and consequently gives the good matching of the experiments. Within the frame of plasticity theory, the detailed constitutive model, the numerical algorithm and the derivation of the tangent stiffness matrix are presented in this study to improve model robustness. This phenomenological model achieved excellent agreement between the experimental and simulation results in element scale respectively for glass fibre-reinforced polymer (GFRP) and carbon fibre-reinforced polymer (CFRP). Moreover, the model is capable of simulating the nonlinear phenomenon of laminates, and good agreement is achieved in nearly all cases.
4 citations