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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: The recently proposed arc-length solver presented in reference May et al. (2016) is reconsidered within the limitations/capabilities of the commercial software packages and recast in a form which is suitable for implementation through user element formalism.
6 citations
TL;DR: In this paper, a 3D macroscopic constitutive law for hysteresis effects in magnetostrictive materials is presented and a finite element implementation is provided and a novel aspect of the thermodynamically consistent model is an additive decomposition of the magnetic and strain field in a reversible and an irreversible part.
Abstract: A 3D macroscopic constitutive law for hysteresis effects in magnetostrictive materials is presented and a finite element implementation is provided The novel aspect of the thermodynamically consistent model is an additive decomposition of the magnetic and the strain field in a reversible and an irreversible part Employing the irreversible magnetic field is advantageous for a finite element implementation, where the displacements and magnetic scalar potential are the nodal degrees of freedom To consider the correlation between the irreversible magnetic field and the irreversible strains a one-to-one relation is assumed The irreversible magnetic field determines as internal variable the movement of the center of a switching surface This controls the motion of the domain walls during the magnetization process The evolution of the internal variables is derived from the magnetic enthalpy function by the postulate of maximum dissipation, where the switching surface serves as constraint The evolution equations are integrated using the backward Euler implicit integration scheme The constitutive model is implemented in a 3D hexahedral element which provides an algorithmic consistent tangent stiffness matrix A numerical example demonstrates the capability of the proposed model to reproduce the ferromagnetic hysteresis loops of a Terfenol-D sample (© 2006 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim)
6 citations
TL;DR: In this article, a computer program has been developed to present a very effective calculation method for structural systems with cable elements using point-based iterative procedure and convergence procedure to prevent excessive displacements through the calculations.
Abstract: Geometric nonlinear static analysis of structural systems with cable elements is carried out using point based iterative procedure. In all sub systems as cable systems, constituted for each node having at least one degree of freedom that is idealized by finite elements, successive calculations are performed. In the analysis part, based on finite element displacement method, to the maximum number of unknown displacements required for each sub-system calculation is limited with three. Tangent stiffness matrix, including pre-stressed internal forces as well as varying geometries with respect to different external force applications, is utilized. The convergence procedure is adapted into the method to prevent excessive displacements through the calculations. In the present study, a computer program has been developed to present a very effective calculation method. Different numerical applications have been considered and the results were compared with the literature results.
Key words: Cable systems, nonlinear analysis, point based iterative procedure, convergence procedure.
6 citations
TL;DR: In this paper, the authors discuss solution schemes for the incremental elastic-plastic structural problem, discretized by means of the Finite Element method, focused on their formulation and implementation in a parallel computing environment.
6 citations
TL;DR: In this article, a stiffened shell element is presented for geometrically non-linear analysis of eccentrically stiffened shells, which is more accurate than with the traditional equivalent orthotropic plate element or with lumping stiffeners.
Abstract: A stiffened shell element is presented for geometrically non-linear analysis of eccentrically stiffened shell structures. Modelling with this element is more accurate than with the traditional equivalent orthotropic plate element or with lumping stiffeners. In addition, mesh generation is easier than with the conventional finite element approach where the shell and beam elements are combined explicitly to represent stiffened structures. In the present non-linear finite element procedure, the tangent stiffness matrix is derived using the updated Lagrangian formulation and the element strains, stresses, and internal force vectors are updated employing a corotational approach. The non-vectorial characteristic of large rotations is taken into account. This stiffened shell element formulation is ideally suited for implementation into existing linear finite element programs and its accuracy and effectiveness have been demonstrated in several numerical examples.
6 citations