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: A nonlinear field theory is derived which admits topological kinks and antikinks as nonlinear excitations but where a topological boundary term breaks the symmetry between the two and energetically favors the kink configuration.
Abstract: We study the dynamical response of a diatomic periodic chain of rotors coupled by springs, whose unit cell breaks spatial inversion symmetry. In the continuum description, we derive a nonlinear field theory which admits topological kinks and antikinks as nonlinear excitations but where a topological boundary term breaks the symmetry between the two and energetically favors the kink configuration. Using a cobweb plot, we develop a fixed-point analysis for the kink motion and demonstrate that kinks propagate without the Peierls-Nabarro potential energy barrier typically associated with lattice models. Using continuum elasticity theory, we trace the absence of the Peierls-Nabarro barrier for the kink motion to the topological boundary term which ensures that only the kink configuration, and not the antikink, costs zero potential energy. Further, we study the eigenmodes around the kink and antikink configurations using a tangent stiffness matrix approach appropriate for prestressed structures to explicitly show how the usual energy degeneracy between the two no longer holds. We show how the kink-antikink asymmetry also manifests in the way these nonlinear excitations interact with impurities introduced in the chain as disorder in the spring stiffness. Finally, we discuss the effect of impurities in the (bond) spring length and build prototypes based on simple linkages that verify our predictions.
26 citations
TL;DR: In this paper, a finite element program is developed by assembling the local stiffness matrices and applying corresponding equivalent nodal stresses, and a design procedure by connecting particle swarm optimization technique with the present finite element analysis is created to reduce the deformations of simply supported composite beams while the quantity of shear connectors remains the same.
25 citations
TL;DR: In this article, a necessary condition for the stability of symmetric pin-jointed structures with kinematic indeterminacy is derived from the positive definiteness of the quadratic form of the tangent stiffness matrix.
25 citations
TL;DR: In this article, a consistent formulation of a tangent stiffness matrix for the geometrically nonlinear analysis of the space beam-column elements allowing for axial-flexural, lateral-torsional and axial torsional buckling is presented.
25 citations
TL;DR: In this paper, the transfer matrix method is adopted to deduce general expressions for the components of the stiffness matrix and equivalent node load vector of non-prismatic members, and the effect of warping is not considered.
Abstract: In this note, the transfer matrix method is adopted to deduce general expressions for the components of the stiffness matrix and equivalent node load vector of nonprismatic members, and the effect of warping is not considered. State vectors are introduced to describe the nodal forces and displacements of a structural member. The relation between the state vectors of the left node and the right node of the member is given by a matrix referred to as the transfer matrix. It is found that the stiffness matrix of the member can be expressed in terms of the transfer matrix. Therefore, an accurate expression for the stiffness matrix can be obtained as long as the corresponding transfer matrix can be accurately determined. The method proposed is a general procedure for the stiffness matrix derivation of both continuous nonprismatic members and discontinuous nonprismatic members. The correctness of the obtained stiffness expressions is verified by two simple numerical examples.
25 citations