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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, a new description method of truss structure based on adjacent matrix and the expression of element stiffness matrix (ESM) containing the joint number is proposed, and a procedure is also given for obtaining a general total stiffness matrix by using the method of large domain transformation matrix (LDTM).
Abstract: This paper proposes a new description method of truss structure based on adjacent matrix and the expression of element stiffness matrix (ESM) containing the joint number. Furthermore a procedure is also given for obtaining a general total stiffness matrix (GTSM) by using the method of large domain transformation matrix (LDTM). GTSM can reduce the difficulty in designing variable geometry trusses.
TL;DR: In this article, a procedure is developed to calculate the stress-strain stiffness matrix from the strains without iteration of the stress components when the material is inelastic, and the stiffness matrices of finite elements are assumed known at one stage of the calculations.
TL;DR: A purely algebraic approach to higher order analysis of (singular) configurations of rigid multibody systems with kinematic loops (CMS) is presented in this article, where rigid body con.gurations are described by elements of the Lie group SE(3) and so the rigid body kinematics is determined by an analytical map f : V SE( 3), where V is the configuration space, an analytic variety.
Abstract: A purely algebraic approach to higher order analysis of (singular) configurations of rigid multibody systems with kinematic loops (CMS) is presented. Rigid body con.gurations are described by elements of the Lie group SE(3) and so the rigid body kinematics is determined by an analytical map f : V SE(3), where V is the configuration space, an analytic variety. Around regular configurations V has manifold structure but this is lost in singular points. In such points the concept of a tangent vector space does not makes sense but the tangent space CqV (a cone) to V can still be defined. This tangent cone can be determined algebraically using the special structure of the Lie algebra se (3), the generating algebra of the special Euclidean group SE (3), and the fact that the push forward map f*, the tangential mapping CqV se (3), is given in terms of the mechanisms screw system. Moreover the differentials of f of arbitrary order can be expressed algebraically. The tangent space to the configuration space can be shown to be a hypersurface of maximum degree 4, a vector space for regular points. It is the structure of the tangent cone to V that gives the complete geometric picture of the configuration space around a (singular) point. Identification of the screw system and its matrix representation with the kinematic basic functions of the CMS allows an automatic algebraic analysis of mechanisms.
01 Dec 2009
TL;DR: In this article, a large deformation finite element analysis is presented for piezoelectric materials and structures, and the results using this user-developed element are found the same as those using this embedded in ABAQUS for geometrical nonlinear analysis.
Abstract: The nonlinear piezoelectric finite element method, which includes geometrical nonlinearity and material nonlinearity, has gained more and more popularity and been studied by more and more researchers. A large deformation finite element analysis is presented for piezoelectric materials and structures in this paper. Green-Lagrenge strains for large deformation are incorporated into the linear piezoelectric equations. The formulations of the secant stiffness matrix and tangent stiffness matrix are presented, and the Newton-Raphson method has been used to solve the nonlinear equations. Based on the finite element package ABAQUS, eight-node plane geometrical nonlinear piezoelectric element is developed. The results using this user-developed element are found the same as those based on the piezoelectric element embedded in ABAQUS for geometrical nonlinear analysis. It indicates that ABAQUS can be used as a convenient platform for developing nonlinear piezoelectric finite element so as to study various nonlinear piezoelectric problems.
TL;DR: In this paper , the authors proposed the use of a new approach to perform a simplified nonlinear analysis using the two-cycle method and a tangent stiffness matrix obtained directly from the homogeneous solution of the problem's (beam-column) differential equation.