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.

Dynamic Analysis of Suspension Bridges and Full Scale Testing

Abstract: This paper is concerned with the earthquake analysis of suspension bridges, in which the effects of large deflections are taken into account. The first part of the study deals with an iteration scheme for the nonlinear static analysis of suspension bridges by means of tangent stiffness matrices. The concept of tangent stiffness matrix is then introduced in the frequency equation governing the free vibration of the system. At any equilibrium stage, the vibrations are assumed to take place tangent to the curve representing the force-deflection characteristics of the structure. The bridge is idealized as a three dimensional lumped mass system and subjected to three orthogonal components of earthquake ground motion producing horizontal, vertical and torsional oscillations. By this means a realistic appraisal is achieved for torsional response as well as for the other types of vibration. The modal response spectrum technique is applied to evaluate the seismic loading for the combination of these vibrations. Various numerical examples are introduced in order to demonstrate the method of analysis. The procedure described enables the designer to evaluate the nonlinear dynamic response of suspension bridges in a systematic manner.

Stiffness modeling for multi-fingered grasping with rolling contacts

Abstract: The stiffness control of an object grasped by a multi-fingered robot hand requires the modeling of the elastic behavior of the object, caused by the stiffness of the fingers. Because of the presence of rolling contacts between the fingers and the object, such a modeling is not a trivial issue, and a very different one from the case of simpler parallel manipulators. We provide here a first expression of the cartesian stiffness matrix produced on the object, as a function of the cartesian stiffness matrices of the fingers, in the case that the contacts are non-sliding point contacts that may freely roll (on the tangent plane) and twist (around the contact normal). We show that this expression of the object-level cartesian stiffness matrix depends also on the contact forces and on the local geometries of the contacting surfaces.

New Formula for Geometric Stiffness Matrix Calculation

Abstract: The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.

Variational Formulation and Symmetric Tangent Operator for Shells with Finite Rotation Field

Abstract: The objective of this paper is to examine the symmetry of the tangent operator for nonlinear shell theories with the finite rotation field. As well known, it has been stated that since the rotation field carries the Lie group structure, not a vector space one, the tangent operator incorporating the rotation field does not become symmetric. In this paper, however, it is shown that by adopting a rotation vector as a variable, the symmetry can be achieved in the Lagrangean (material) description. First, we present a general concept for the problem. Next, we adopt the finitely deformed thick shell problem as an example. We also present a tensor formula that plays a key role for the derivation of a symmetric tangent operator. keyword: finite rotation, tangent operator, symmetry, shell theory, variational formulation.