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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 article, a mesh-free co-rotational formulation for two-dimensional continua is proposed, where the motion of a body is separated into rigid motion and strain-producing deformation.
Abstract: In this paper, a meshfree co-rotational formulation for two-dimensional continua is proposed. In a co-rotational formulation, the motion of a body is separated into rigid motion and strain-producing deformation. Traditionally, this has been done in the setting of finite elements for beams and shell-type elements. In the present work every node in a meshfree discretized domain has its own co-rotating coordinate system. Three key ingredients are established in order to apply the co-rotational formulation: (i) the relationship between global and local variables, (ii) the angle of rotation of a typical co-rotating coordinate system, and (iii) a variationally consistent tangent stiffness matrix. An algorithm for the co-rotational formulation based on load control is provided. Maximum-entropy basis functions are used to discretize the domain and stabilized nodal integration is implemented to construct the global system of equations. Numerical examples are presented to demonstrate the validity of the meshfree co-rotational formulation. Copyright © 2009 John Wiley & Sons, Ltd.
28 citations
TL;DR: In this paper, a continuous sensitivity equation (CSE) was developed in local derivative form for fluid-structure shape design problems, where the boundary velocity method was used to derive the continuum sensitivity equations and sensitivity boundary conditions for built-up joined beam structure under transient aerodynamic loads.
28 citations
TL;DR: In this paper, an adaptive non-stationary load sweeping algorithm was developed to investigate post-buckling dynamics and mode jumping phenomena of generally loaded thin plates in a global context, which can avoid spurious convergence of the transient response to an unstable equilibrium.
28 citations
TL;DR: In this article, a mixed finite element (FE) procedure of the gradient Cosserat continuum for the second-order computational homogenisation of granular materials is presented, where translational displacements, microrotations, and displacement gradients with Lagrange multipliers are taken as independent nodal variables.
Abstract: A mixed finite element (FE) procedure of the gradient Cosserat continuum for the second-order computational homogenisation of granular materials is presented. The proposed mixed FE is developed based on the Hu---Washizu variational principle. Translational displacements, microrotations, and displacement gradients with Lagrange multipliers are taken as the independent nodal variables. The tangent stiffness matrix of the mixed FE is formulated. The advantage of the gradient Cosserat continuum model in capturing the meso-structural size effect is numerically demonstrated. Patch tests are specially designed and performed to validate the mixed FE formulations. A numerical example is presented to demonstrate the performance of the mixed FE procedure in the simulation of strain softening and localisation phenomena, while without the need to specify the macroscopic phenomenological constitutive relationship and material failure model. The meso-structural mechanisms of the macroscopic failure of granular materials are detected, i.e. significant development of dissipative sliding and rolling frictions among particles in contacts, resulting in the loss of contacts.
28 citations
TL;DR: In this paper, a top-down design method for the stiffness of precision machine tools that considers the entire machine stiffness to guarantee the stiffness requirements in the initial design stage is presented.
Abstract: This work describes a new top-down design method for the stiffness of precision machine tools that considers the entire machine stiffness to guarantee the stiffness requirements in the initial design stage A stiffness modelling method and a stiffness matching design method are presented to achieve the top-down design of the stiffness A new stiffness characterisation using the stiffness coefficients for characterising the stiffness of the structural parts and the functional units is proposed The deformation model of the entire machine is established based on multi-body system theory, and the equations of the stiffness coefficients for the deformations of the components are established based on the simultaneous equations of the static equilibrium equations, the deformation compatibility equations and the physical equations The three-direction (3D) stiffness model is obtained by substituting the equations into the deformation model that reflects the stiffness characteristics of the machine tool Thus, the reliability of the stiffness model is verified by experiments Next, the stiffness matching design is performed to confirm the reasonable stiffness values of the parts based on the stiffness model The finite element method (FEM) is used to validate the proposed method The contribution rate of the stiffness of the parts to the stiffness of the entire machine is analysed
28 citations