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.
Papers published on a yearly basis
Papers
More filters
01 Jan 1999
TL;DR: A dynamic model for gear transmissions acting around a static working point, and taking into account the complete mechanical components is described, providing global dynamic behaviour of automobile gearboxes and consequences of technological choices could be evaluated.
Abstract: This paper describes a dynamic model for gear transmissions acting around a static working point, and taking into account the complete mechanical components. Gearbox casing behavior is introduced by using substructure analysis, and a tangent stiffness matrix could be defined for each roller body bearing element. This model is used to study the dynamic behaviour of an automobile gearbox. The first studies highlight the influence of the roller bearings on the dynamic behaviour of the kinematic chain and show that the bearings have to be modelled accurately. In a second step, the flexible casing of the gearbox is taken into account and dynamic couplings between deformations of the casing and the kinematic chain are evaluated. As a result of these works, global dynamic behaviour of automobile gearboxes can be provided and consequences of technological choices could be evaluated.
05 Mar 2006
TL;DR: In this article, the authors derived a non-symmetric stiffness matrix for a robotic mechanism and presented a novel synthesis procedure for the desired non-smooth stiffness matrix of a planar structure when the structure is not in equilibrium.
Abstract: The compliance/stiffness of a robotic mechanism is usually modeled by a 6 by 6 symmetric positive definite matrix at an equilibrium point using screw theory. When an external wrench is exerted on the mechanism and the mechanism moves away from its equilibrium, the modeled compliance/stiffness matrix becomes non-symmetric. In this article, the authors derive a non-symmetric stiffness matrix for a robotic mechanism and present a novel synthesis procedure for the desired non-symmetric stiffness matrix of a planar structure when the structure is not in equilibrium
TL;DR: In this article, a negative stiffness (matrix) is introduced to take the effect of axial loads on the stiffness of the system into account and the stiffness matrix is modified by this negative stiffness matrix.
Abstract: Presented in this paper is a simple and practical method for buckling analysis of the overall structural system. The method is developed from the idea that the stiffness (for a SDOF system) or determinant of stiffness matrix (for a MDOF system) is getting to zero as the system is loaded to bucking mode, or the loads reaches the buckling load of the system. A negative stiffness (matrix) is introduced to take the effect of axial loads on the stiffness (matrix) of the system into account and the stiffness (matrix) is modified by this negative stiffness (matrix). To get the buckling load of the overall system, first order analysis (P-Δeffect) is performed with a simple method suggested. The second order analysis (P-δ) is performed by the introducing of a force modification factor to modify the buckling load from first order analysis. Application examples are presented and the results are compared with result obtained from system buckling analysis with FEA. The simplicity, effectiveness and the accuracy of the suggested method is demonstrated.
TL;DR: In this paper, the relationship between the stress rate and the tangent stiffness was derived using the special orthogonal group SO (3) in the finite element formulation, and the stiffness elements were given.
Abstract: In the previous paper, the relationship between the stress rate and the tangent stiffness was derived using the special orthogonal group SO (3) in the finite element formulation. The stress rates used are the Truesdell stress rate, the Jaumann stress rate, the Neo-Green stress rate and the Ishihara stress rate. In this work, the stiffness elements of the tangent stiffnesses of beam elements with SO (3) are given. These elements include material stiffness ΔδПm, geometric stiffness of rigid rotation ΔδП10, geometric stiffness of stretch to stress direction ΔδПsg, stress, geometric stiffness of stretch perpendicular to area ΔδПsg, area and geometric stiffness of stretch to deformation rate ΔδПsg, deform. In a future paper, the tangent stiffness of these stress rates of a beam element will be given.
01 Jan 2000
TL;DR: A shape design sensitivity analysis and optimization of structural transient dynamics are proposed for the finite deformation elastoplastic materials under impact with a rigid surface in this paper, where a shape variation of the structure is considered using the material derivative approach in continuum mechanics.
Abstract: A shape design sensitivity analysis and optimization of structural transient dynamics are proposed for the finite deformation elastoplastic materials under impact with a rigid surface. A shape variation of the structure is considered using the material derivative approach in continuum mechanics. A penalty method, modified Coulomb friction law, and the slave—master concept are used for the impact problem. Hyperelasticity-based multiplicatively decomposed elastoplasticity is used for the constitutive model. The implicit Newmark time integration scheme is used for the structural dynamics. The design sensitivity equation is solved at each converged time step with the same tangent stiffness matrix as response analysis without iteration. The cost of sensitivity computation is more efficient than the cost of response analysis for the implicit time integration method. The efficiency and the accuracy of the proposed method are shown through the design optimization of a vehicle bumper.