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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19 Sep 2001
TL;DR: In this paper, the buckling moment of doubly symmetric spatial beams under different types of end bending moment and compressive axial force was investigated using finite element method using co-rotational total Lagrangian finite element formulation.
Abstract: The buckling moment of doubly symmetric spatial beams under different types of end bending moment and compressive axial force is investigated using finite element method. A co-rotational total Lagrangian finite element formulation is employed here. An incremental-iterative method based on the Newton-Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. Numerical examples are presented to investigate the effect of compressive force on the buckling moment of spatial beams under different types of bending moment.
01 Jan 2006
TL;DR: This paper presents a new method to separate the torque from each pathway from the total torque measurement, and uses a subspace based system identification method to estimate the dynamics of each pathway directly from measured data without iteration.
Abstract: Joint stiffness, defined as the relation between the angular position of a joint and the torque acting about it, can be used to describe the dynamical behavior of the human ankle during posture and movement. Joint stiffness can be separated into intrinsic stiffness and reflex stiffness, which are modeled as a linear system and a Hammerstein system, respectively. A two-pathway parallel cascade model, with the intrinsic stiffness on one pathway and the reflex stiffness on the other, can be used to describe the joint stiffness. In this paper, we present a new method to separate the torque from each pathway from the total torque measurement. A subspace based system identification method is used to estimate the dynamics of each pathway directly from measured data without iteration. Simulation studies demonstrate that the method produces accurate results without the need of iteration.
TL;DR: In this article , an analytical method for obtaining an explicit expression of stress increments in terms of stresses, deformations, strain increments, temperature increments, and temperature is presented. But the analysis is limited to the case of thin-walled elements.
Abstract: The equations of the combined model of phase and structural deformation of shape memory alloys (SMA) express the increments of deformations in terms of the increments of stresses, martensite volume part parameter and temperature, stresses themselves, deformations, and the temperature. However, to solve the stability problems of long-or thin-walled elements from SMA, as well as to formulate the tangent stiffness matrix of the finite element method for SMA, it is necessary to have an explicit expression of stress increments in terms of stresses, deformations, strain increments, temperature increments, and temperature. The paper presents an analytical method for obtaining such inverting.
TL;DR: In this paper , the authors studied the incremental stiffness of a composite and showed that it is equivalent to a strengthened form of uniform infinitesimal polyconvexity and is independent of the geometry.
Abstract: Abstract Bounds to the overall stiffness of a composite are well-known within the classical theory of elasticity. They are based on the positive-definiteness of the local stiffness. A transfer to a prestressed state is not trivial. We may study the incremental stiffness that connects the nominal stress rate with the velocity gradient. But when there are mainly compressive stresses, then positive-definiteness can only be secured if this stiffness is replaced by a pseudo-stiffness. Its existence is equivalent to a strengthened form of uniform infinitesimal polyconvexity and is independent of the geometry. The same is the case with the crude Voigt and Reuss bounds. More refined kinematic or dynamic approximations do, of course, depend on the geometry. This is demonstrated with the unidirectional reinforcement of a matrix.
TL;DR: In this article, a new mathematical algorithm has been developed for the tangent, which guarantees that the error is zero at 0°, 45°, and 90° corresponding to tangents of 0, 1, and infinity.
Abstract: A new mathematical algorithm has been developed for the tangent. The form of the equation guarantees that the error is zero at 0°, 45°, and 90° corresponding to tangents of 0, 1, and infinity. With only one constant the error is brought to zero at two more points and the maximum error is less than one part in 3000. By adding a second constant, the error is reduced to less than one in 720 000. Further terms improve the accuracy geometrically.