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 article, the authors investigated the overall viscoelastic responses and stability of a hexagonal lattice cell containing pre-chosen negative stiffness components and showed that the stiffness and damping anomalies in terms of peaks and anti-peaks are observed in the metastable regime when the amount of negative stiffness is selectively tuned.
Abstract: The overall viscoelastic responses and stability were investigated of a hexagonal lattice cell containing pre-chosen negative stiffness components. The study was motivated by the need for fundamental understanding of negative stiffness effects on structures consisting of many degrees of freedom, as well as the symmetry of the structures. Theoretically, use of negative stiffness inclusions to obtain high stiffness and high damping composites has been extensively studied in Hashin-Shtrikman models and one-dimensional discrete systems. Studies on two-dimensional structures containing negative stiffness components and their stability are limited. The finite-element method, combined with the technique of the state space representation, was used to analyze two-dimensional, nested hexagons composed of two-force components that obey the constitutive relation of the standard linear solid. Effective stiffness and damping anomalies in terms of peaks and anti-peaks are observed in the metastable regime when the amount of negative stiffness is selectively tuned. According to the Lyapunov indirect stability theorem, the system as a whole is stable when the tuning stiffness is greater than a critical negative value, but metastable otherwise. The degree of metastability depends on viscosity in the components. Furthermore, stiffness anomalies may be easier to observe experimentally from compression tests than hydrostatic or shear tests.
9 citations
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TL;DR: In this paper, a simplified co-rotational formulation for quadrilateral shell elements inheriting the merit of element-independence from the traditional corotational approach in literature is presented, with the objective of application to nonlinear analysis of civil engineering structures.
Abstract: Summary
This paper presents a simplified co-rotational formulation for quadrilateral shell elements inheriting the merit of element-independence from the traditional co-rotational approach in literature. With the objective of application to nonlinear analysis of civil engineering structures, the authors further simply the formulation of the geometrical stiffness using the small strain assumption which is valid in the co-rotational approach, with the warping effects considered as eccentricities. Compared with the traditional element-independent co-rotational method, the projector is neglected both in the tangent stiffness matrix and the internal force vector for simplicity in formulation. Meanwhile, a quadrilateral flat shell element allowing for drilling rotations is adopted and incorporated into this simplified co-rotational algorithm for geometrically nonlinear analysis involved with large displacements and large rotations. Several benchmark problems are presented to confirm the efficiency and accuracy of the proposed method for practical applications.
9 citations
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TL;DR: In this article, the authors developed a new method for finding multiple bifurcation points in structures by using eigenvalue perturbation of tangent stiffness matrix, and obtained the load parameter associated with multiple Bifurcation points.
Abstract: Purpose – The aim of this paper is to develop a new method for finding multiple bifurcation points in structures.Design/methodology/approach – A brief review of nonlinear analysis is presented. A powerful method (called arc‐length) for tracing nonlinear equilibrium path is described. Techniques for monitoring critical points are discussed to find the rank deficiency of the stiffness matrix. Finally, by using eigenvalue perturbation of tangent stiffness matrix, load parameter associated with multiple bifurcation points is obtained.Findings – Since other methods of finding simple bifurcation points diverge in the neighborhood of critical points, this paper introduces a new method to find multiple bifurcation points. It should be remembered that a simple bifurcation point is a multiple bifurcation point with rank deficiency equal to one. Therefore, the method is applicable to simple critical points as well.Practical implications – Global buckling of the structures should be considered in design. Many structu...
9 citations
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TL;DR: In this paper, a continuation algorithm based on the Asymptotic Numerical Method (ANM) was proposed to study instability phenomena of large torsion of thin-walled open sections beams under various external loadings.
9 citations
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TL;DR: In this paper, a modified Newton's method is proposed to simultaneously set the residual force and the minimum eigenvalue of the tangent stiffness matrix to zero by using an iterative algorithm.
9 citations