Showing papers on "Tangent stiffness matrix published in 1994"
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TL;DR: In this article, a complete potential based framework using internal state variables is put forth for the derivation of reversible and irreversible constitutive equations, where the existence of the total (integrated) form of either the Helmholtz free energy or the Gibbs complementary free energy are assumed a priori.
78 citations
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TL;DR: In this paper, a general framework for the derivation of the stress tensor and the tangent moduli for invariant-based models, for both the reference and the current configuration, is presented.
Abstract: The paper starts with a review of constitutive equations for rubber‐like materials, formulated in the invariants of the right Cauchy—Green deformation tensor A general framework for the derivation of the stress tensor and the tangent moduli for invariant‐based models, for both the reference and the current configuration, is presented The free energy of incompressible rubber‐like materials is extended to a compressible formulation by adding the volumetric part of the free energy In order to overcome numerical problems encountered with displacement‐based finite element formulations for nearly incompressible materials, three‐dimensional finite elements, based on a penalty‐type formulation, are proposed They are characterized by applying reduced integration to the volumetric parts of the tangent stiffness matrix and the pressure‐related parts of the internal force vector only Moreover, hybrid finite elements are proposed They are based on a three‐field variational principle, characterized by treating th
53 citations
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TL;DR: In this paper, a simple four-noded geometrically nonlinear shell element is presented, which handles arbitrarily large displacements and rotations, based on the assumption of small incremental strain in each load step, a corotational procedure is employed to extract the pure deformational displacements, and update element stresses and internal force vectors through a piecewise linearized strain-displacement relation.
49 citations
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TL;DR: In this article, a plane-strain implicit dynamic finite element formulation is applied for the analysis of sheet-forming processes, where the material is assumed to follow a power law of hardening with strain-rate sensitivity once the initial elastic limit strain is reached.
27 citations
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TL;DR: In this paper, a finite element model based on a Reissner-Mindlin theory involving von Karman nonlinearity is developed for the analysis of axially compressed plates in the static elastic conservative cases.
22 citations
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TL;DR: In this article, a co-rotational, updated Lagrangian formulation for geometrically nonlinear analysis of shells is presented, which is ideally suited for implementation in existing linear finite element programs and has been demonstrated by a number of numerical examples.
18 citations
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TL;DR: In this paper, a comparison of implementations of consistent tangent operators that arise in implicit integration of Von Mises and Drucker-Prager yield criteria is made, and the consequences of different formulations of the tangent operator on the numerical accuracy are assessed.
Abstract: A comparison is made of implementations of consistent tangent operators that arise in implicit integration of Von Mises and Drucker-Prager yield criteria. When computing the consistent tangent operator a matrix inversion has to be performed at integration point level. The consequences of different formulations of the consistent tangent operator on the numerical accuracy are assessed.
11 citations
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TL;DR: In this paper, the consistent co-rotational beam formulation has been modified to include inelastic deformation using a sublayer material model and an explicit tangent stiffness matrix for a non-conservative beam was consistently derived from the assumed beam kinematics.
Abstract: The consistent co-rotational beam formulation has been modified to include inelastic deformation using a sublayer material model. An explicit tangent stiffness matrix for a non-conservative beam was consistently derived from the assumed beam kinematics. Several example problems were solved to verify the formulation and, subsequently, a comparative study was carried out to examine the validity of the von Karman theory in large deflection analysis. It is found that the presence of beam axial constraint plays an important role on the performance of the von Karman approximation. In general, the von Karman formulation can provide reasonable solutions to large deformation problems of extensional structures, but its performance becomes unsatisfactory for the inextensional case even under relatively small deflections.
8 citations
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TL;DR: In this article, it was demonstrated that the use of the tangent plane representation in the geometric stiffness matrix is far superior to the common form at present, and it was also shown that the geometric stiffness matrix can be formulated by use of either of the two rotation representations.
Abstract: In the formulation of the semi-Loof element the rotation of the tangent plane is derived from the interpolation of the transverse displacement, while the rotation of the normal is interpolated separately by another set of shape functions. The geometric stiffness matrix can be formulated by use of either of the two rotation representations. It is demonstrated that the use of the tangent plane representation in the geometric stiffness matrix is far superior to the common form at present.
5 citations
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TL;DR: In this article, a consistent stiffness matrix for the generalized trapezoidal rule is derived for the von Mises material model with mixed isotropic/kinematic hardening.
4 citations
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TL;DR: In this article, a variational formulation of time-independent supercontivity for a Ginzburg-Landau superconductor was developed for the general three-dimensional case and specialized to one-dimensional cases.
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TL;DR: In this article, an incremental-iterative nonlinear solution technique for solving the nonlinear finite element equations of the superconducting state of a superconductor is presented. But the proposed solution is difficult to solve within the typical 16-place double precision supplied by most computers.
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TL;DR: In this article, the authors propose a framework to improve the quality of the data collected by the data collection system. But they do not specify the criteria for the evaluation of the collected data.
Abstract: 本文提出了一致切线刚度法,并把它应用于三维弹塑性有限元分析问题。从而解决了增量迭代弹塑性有限元分析方法中长期存在的速度慢、精度低问题,一致切线刚度法满足加卸载互补准则,即没有应力漂移现象,具有一阶精度、二阶迭代收敛速度、计算量少和无条件稳定等优点,借助算例对一致切线刚度法和传统切线刚度法(包括路径相关和路径无关两种结构变量更新格式)从计算精度、迭代收敛速度和计算量等几方面进行了比较。
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TL;DR: In this paper, a generalization of the stability analysis is presented: analogously to the stabilisation analysis of equilibrium, stability analysis of compatibility, based on the complementary energy will be introduced, and the concept of tangent and compliance modulus is applied.
Abstract: A generalization of the stability analysis is presented: analogously to the stability analysis of equilibrium, based on the potential energy, stability analysis of compatibility, based on the complementary energy will be introduced.
Nonlinearly inelastic material is considered, excluding strain softening and damage but including strain hardening and locking. The concept of tangent and compliance modulus is applied.
Global stability analysis is investigated, related to the total domain of the state variables,distinguishing the dead and rigid type of load, and their relation with the basic variational principles.
Discrete structural model of frame structures with uniaxial nonlinear and nonelastic material behaviour will be analysed.
Numerical illustrations can be studied in the author's papers, in (KURUTZ 1989, 1993, 1994).
01 Jan 1994
TL;DR: In this paper, a complete potential based framework utilizing internal state variables is put forth for the derivation of reversible and irreversible constitutive equations, where the existence of the total (integrated) form of either the Helmholtz free energy or the Gibbs complementary free energy are assumed a priori.
Abstract: A complete potential based framework utilizing internal state variables is put forth for the derivation of reversible and irreversible constitutive equations. In this framework, the existence of the total (integrated) form of either the (Helmholtz) free energy or the (Gibbs) com- plementary free energy are assumed a priori. Two options for describing the flow and evolu- tionary equations are described, wherein option one (the fully coupled form) is shown to be over restrictive and the second option (the decoupledform) provides significant flexibility. As a con- sequence of the decoupled form, a new operator, that is, the compliance operator, is defined, which provides a link between the assumed Gibb's and complementary dissipation potential and ensures a number of desirable numerical features, for example, the symmetry of the resulting consistent tangent stiffness matrix. An important conclusion reached is that although many theo- ries in the literature do not conform to the general potential framework outlined, it is still pos- sible in some cases, by slight modifications of the employed forms, to restore the complete potential structure.