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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 article , a generalized line-element formulation was proposed for geometrically nonlinear analysis of tapered steel members with nonsymmetric cross-sections to assess the member buckling behaviors.
1 citations
TL;DR: In this paper, an analytical formulation of the generalized stress-strain relationships for biaxially loaded column segments is presented; the generalized stresses are an axial force, two bending moments about the principal axes, and a bimoment.
Abstract: An analytical formulation of the generalized stress-strain relationships for biaxially loaded column segments is presented. The generalized stresses are an axial force, two bending moments about the principal axes, and a bimoment. The corresponding generalized strains are an axial strain at the centroid, two bending curvatures, and a warping curvature. The material characteristics are assumed to be trilinear, i.e., elastic, plastic, and linear strain hardening. Elastic unloading of yielded fibers and “Bauschinger effects” are included in the analysis. Based upon the equations formulated, a computer program was developed to provide numerical results. The element of the tangent stiffness matrix was evaluated numerically by dividing the wide flange section into finite element.
1 citations
TL;DR: Kirchhoff et al. as mentioned in this paper proposed a method to solve the problem of "missing links" in the context of mobile phones, which can be found here: https://www.youtube.com/watch.
Abstract: 本論文では, 全ラグランジュ表記法によるハイアラーキ平面シェル要素とソリッド要素の接線剛性行列を求め, 線形座屈理論に基づいたハイアラーキ要素による座屈解析法を開発する. 本解析法の精度を調べるために平板の座屈解析を行って, 提案する要素と各非線形項の影響を検討する. 平板の解析では, 一般に Kirchhoff 理論, Mindlin 理論と3次元弾性論が用いられるが, ハイアラーキ要素による解法では, それぞれの理論解に対して高精度の値が得られることを示す. また, 実用的な観点から, 計算効率の良い Mindlin 要素を用いて, 弾性論による解に匹敵する値が得られるせん断補正係数を提案する.
1 citations
01 Jan 1999
TL;DR: In this article, an imperfect beam-column element for second-order analysis of two-and three-dimensional frames is presented, where the initial imperfection of element is restricted to a curvature in the form of a single sinusoidal half-wave.
Abstract: Publisher Summary
This chapter presents the imperfect beam-column element for second-order analysis of two- and three-dimensional frames. The initial imperfection of element is restricted to a curvature in the form of a single sinusoidal half-wave. The simplest and most typical stiffness matrix method of analysis is to extend the cubic Hermite element to the nonlinear case by inclusion of the geometric stiffness to the linear stiffness matrix, to form the tangent stiffness matrix. The method of stability function is employed as an exact solution of the beam-column. The method develops the element matrix by solving the differential equilibrium equation of a beam-column under the action of axial load. The accuracy of the analysis using stability function is affected only by the numerical truncating error. The exact stiffness matrix of an imperfect member under a large axial force is derived and incorporated into a second-order analysis computer program, Nonlinear Integrated Design and Analysis (NIDA), for analysis of skeletal structures. The element is accurate even when the axial force is four times the Euler's buckling load, which refers to the extreme case of buckling in a column with both ends fixed in direction and in rotation.
1 citations
TL;DR: In this article, the Co-rotational formulation is used to predict the flexural-torsional buckling loads for spatial structures in which the nodal forces and moments on the rigid body rotation are modeled.
Abstract: Geometrically nonlinear analysis of 3D framed structures has focused on the treatment of the difficulties associated with finite nodal rotations. The Co-rotational formulation excludes the rigid body rotation of the element, and to account for this aspect the addition of a stability matrix is required to the natural tangent stiffness matrix. This spatial beam element stability matrix needs to fully account for the behaviour of the nodal forces and moments on the rigid body rotation. In the context of the Co-rotational formulation, the correct stability matrix is used in conjunction with the natural tangent stiffness matrix. The natural finite element concept used for the numerical analysis of nonlinear structural problems is extended to the Co-rotational formulation. It is shown through numerical examples that fully account for the rotational behaviour of nodal moments, that the Co-rotational formulation can accurately predict the flexural-torsional buckling loads for spatial structures in which the membe...
1 citations