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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: In this paper, the stiffness property of a rapidly rotating gyroscope is described by using a separation of variables as is done in problems on stability with respect to a part of the variables.
TL;DR: In this paper, the authors define a cone of tangent vectors of the reachable set of a control system which is a regular tangent cone and show that the Lagrange multiplier rule applies so that an high order Maximum Principle for Mayer optimization control problem with constraints on the final point can be stated.
01 Jan 2009
TL;DR: In this paper, the local tangent stiffness matrix of a plane frame member is derived by differentiating the member resistance vector in the displaced position, which facilitates an analysis using only one element per member.
Abstract: SECOND-ORDER STRUCTURAL ANALYSIS WITH ONE ELEMENT PER MEMBER Jesse W. Lyon Department of Civil and Environmental Engineering Master of Science In this thesis, formulas for the local tangent stiffness matrix of a plane frame member are derived by differentiating the member resistance vector in the displaced position. This approach facilitates an analysis using only one element per member. The formulas are checked by finite difference. The derivation leads to the familiar elastic and geometric stiffness matrices used by other authors plus an additional higher order geometric stiffness matrix. Contributions of each of the three sub-matrices to the tangent stiffness matrix are studied on both the member and structure levels through two numerical examples. These same examples are analyzed three different ways for comparison. First, the examples are analyzed using the method presented in this thesis. Second, they are analyzed with the finite element modeling software ABAQUS/CAE using only one element per member. Third, they are analyzed with ABAQUS using 200 elements per member. Comparisons are made assuming the ABAQUS analysis which uses 200 elements per member is the most accurate. The element presented in this thesis performs much better than the ABAQUS analysis which uses one element per member, with maximum errors of 1.0% and 40.8% respectively, for a cantilever column example. The maximum error for the two story frame example using the ABAQUS analysis with one element per member is 42.8%, while the results from the analysis using the element presented in this thesis are within 1.5%. Using the element presented in this thesis with only one element per member gives good and computationally efficient results for second-order analysis.
TL;DR: In this article, the occurrence and non occurrence of low-frequency stick-slip motion on a simple caliper-slider experimental model was discussed. But the analysis focused on the relationship between stiffness, i.e., contact stiffness and structure stiffness, and the generation of stick-slip motion.
Abstract: This paper discusses the occurrence and non occurrence of low-frequency stick-slip motion on a simple caliper-slider experimental model. The analysis focused on the relationship between stiffness, i.e. contact stiffness and structure’s stiffness, and the generation of stick-slip motion. The occurrence of stick-slip motion is determined by analyzing the frequency characteristic of resulted vibration acceleration at the beginning of sliding which is resulted from a simultaneous application of force in tangential direction and slow release of force in normal direction. The results show that the occurrence and non occurrence of stick-slip motion can be classified into three regions according to the parameter of stiffness ratio, i.e. non occurrence region, mixed region, and occurrence region. The stiffness ratio Sr, the ratio of contact stiffness Kc to structure’s stiffness Ks, of 40 is found to be critical for the low-frequency stick-slip generation in this experimental model.
24 Apr 2006
TL;DR: In this paper, a strong coupled formulation is proposed and a tangent stiffness matrix of the whole problem is computed using this matrix, nonlinear algorithms such as the Riks-Crisfield algorithm may be applied to solve the static nonlinear problem and determine accurately the static pull-in voltage.
Abstract: This paper presents the advantages of a strong coupled formulation to model the electro-mechanical coupling appearing in MEMS. Usually the classical softwares use a staggered methodology iterating between two different codes to obtain the solution of the coupled problem. In this research a strong coupled formulation is proposed and a tangent stiffness matrix of the whole problem is computed. Using this matrix, nonlinear algorithms such as the Riks-Crisfield algorithm may be applied to solve the static nonlinear problem and determine accurately the static pull-in voltage. Moreover, the natural frequencies may be computed around each equilibrium positions. The dynamic behaviour of the structure may also be studied and two new parameters are defined: the dynamic pull-in voltage and the dynamic pull-in time. This strong coupled methodology deriving from variational principle may also be used for topology optimisation and extended finite elements.