Showing papers on "Tangent stiffness matrix published in 2003"
TL;DR: In this article, a thermodynamically consistent nonlocal damage model is proposed to solve the softening ill-posed continuum problem, where the nonlocal integral operator is applied consistently to the damage variable and its thermodynamic conjugate force, i.e. nonlocality is restricted to internal variables only.
166 citations
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TL;DR: In this article, it was shown that if a is any positive number other than 1, the tangent line to the curve y = ax at the point (/ In a, e) goes through the origin.
Abstract: It was noted in [1] that if a is any positive number other than 1, the tangent line to the curve y = ax at the point (/ In a, e) goes through the origin. The interesting feature here is that the y-coordinate is independent of a. We will show that this result is not as unique as it initially appears; there are many families of curves whose tangent lines at a fixed y-coordinate go through the origin. Shifting attention to the x-coordinate, it turns out that families of curves whose tangent lines at a fixed x-coordinate go through the origin have some interesting properties. In particular, these functions form the kernel of a linear transformation. The tangent line to a differentiable function f at the point (c, f(c)) with c :i 0 goes through the origin if and only if f'(c) = f(c)/c. By shifting, scaling, and tilting a given graph, it is possible to make the modified graph have a tangent line go through the origin at any given value of x or y. These geometric operations on a graph can be performed by modifying the original function by linear factors. This is the main idea used in the next paragraph. Let (a, b) be an open interval that contains the number 1. Suppose that f is differentiable and strictly increasing on (a, b) and that f'(1) < e. (There is nothing special about the choice of the numbers 1 and e; they could be replaced with any positive real numbers.) For each c :f 0, define a function gc on the open interval with endpoints ca and cb by
130 citations
TL;DR: In this paper, the implicit integration and consistent tangent modulus of an inelastic constitutive model with transient and steady strain rates, both of which are time and temperature-dependent, are presented.
Abstract: This paper describes the implicit integration and consistent tangent modulus of an inelastic constitutive model with transient and steady strain rates, both of which are time- and temperature-dependent; the transient rate is influenced by the evolution of back stress decomposed into parts, while the steady rate depends only on applied stress and temperature. Such a non-unified model is useful for high-temperature structural analysis and is practical owing to the ease in determining material constants. The implicit integration is shown to result in two scalar-valued coupled equations, and the consistent tangent modulus is derived in a quite versatile form by introducing a set of fourth-rank constitutive parameters into the discretized evolution rule of back stress. The constitutive model is, then, implemented in a finite element program and applied to a lead-free solder joint analysis. It is demonstrated that the implicit integration is very accurate if the multilinear kinematic hardening model of Ohno and Wang is employed, and that the consistent tangent modulus certainly affords quadratic convergence to the Newton–Raphson iteration in solving nodal force equilibrium equations. Copyright © 2003 John Wiley & Sons, Ltd.
80 citations
TL;DR: The stiffness synthesis problem of variable geometry double planar parallel robots is addressed through the use of Gröbner bases that determine the solvability of the stiffness synthesis polynomial systems and by transforming these systems into corresponding eigenvalue problems using multiplication tables.
Abstract: In this paper, we address the stiffness synthesis problem of variable geometry double planar parallel robots. For a desired stiffness matrix, the free geometrical variables are calculated as a solution of a corresponding polynomial system. Since in practice the set of free geometrical variables might be deficient, the suggested solution addresses also the case where not all stiffness matrix elements are attainable. This is done through the use of Grobner bases that determine the solvability of the stiffness synthesis polynomial systems and by transforming these systems into corresponding eigenvalue problems using multiplication tables. This method is demonstrated on a novel variable geometry double planar six-degrees-of-freedom robot having six free geometric variables. A solution of the double planar stiffness synthesis problem is obtained through decomposing its stiffness matrix in terms of the stiffness matrices of its planar units. An example of this procedure is presented in which synthesizing six el...
59 citations
TL;DR: In this paper, the effect of a two-degree-of-freedom system kinematically connected to the beam is represented exactly by replacing it with equivalent stiffness coefficients, which are added to the appropriate stiffness coefficients of the bare beam.
Abstract: This paper is concerned with the dynamic stiffness formulation and its application for a Bernoulli-Euler beam carrying a two degree-of-freedom spring-mass system. The effect of a two degree-of-freedom system kinematically connected to the beam is represented exactly by replacing it with equivalent stiffness coefficients, which are added to the appropriate stiffness coefficients of the bare beam. Numerical examples whose results are obtained by applying the Wittrick-Williams algorithm to the total dynamic stiffness matrix are given and compared with published results. Applications of the theory include the free vibration analysis of frameworks carrying two degree-of-freedom spring-mass systems.
26 citations
TL;DR: In this article, a nonlinear dynamic finite element technique is developed to analyze the elastoplastic dynamic response of single-layer reticulated shells under strong earthquake excitation, in which the nonlinear three-dimensional beam elements are employed.
20 citations
TL;DR: In this paper, a unified approach is presented in such a way that a simple closed-form expression gives the consistent tangent matrix for the classical constitutive relations (von Mises, Tresca, Mohr-Coulomb, Drucker-Prager).
Abstract: The return mapping algorithm is one of the most efficient procedures to solve elasto-plastic problems. However, a criticism that may be lodged against this method is the difficulty of the practical computation of the consistent tangent matrix when the return is non-radial. Much research has been done to handle this matrix. In this paper, a unified approach is presented in such a way that a simple closed-form expression gives the consistent tangent matrix for the classical constitutive relations (von Mises, Tresca, Mohr–Coulomb, Drucker–Prager). The basic ideas are in the properties of eikonal equations appearing in several fields as image treatment, short time computation in elastic waves and others. The same kinds of ideas can be extended to non-classical models. Copyright © 2003 John Wiley & Sons, Ltd.
16 citations
07 Apr 2003
TL;DR: In this article, a new modification scheme of the stress-strain tensor is presented for finite element analysis of wrinkled membranes, which is strictly based on tension field theory and leads to precise tangent stiffness matrix in the sense that the changes in the wrinkling direction and the amount of wrinkliness are both taken into account.
Abstract: A new modification scheme of the stress-strain tensor is presented for finite element analysis of wrinkled membranes. The scheme is strictly based on tension field theory. Modified stress-strain tensor leads to precise tangent stiffness matrix in the sense that the changes in the wrinkling direction and the amount of wrinkliness are both taken into account. Two numerical examples are presented to demonstrate the effectiveness and robustness of the scheme in the finite element analysis of partly wrinkled membranes.
11 citations
31 Jul 2003
TL;DR: In this article, a model for the strong electro-mechanical coupling appearing in micro-electro-machined systems (MEMS) is presented. But the authors focus on the non-linear variation of frequencies with respect to voltage and stiffness until pull-in appears.
Abstract: A modeling procedure is proposed to handle the strong electro-mechanical coupling appearing in micro-electro-mechanical systems (MEMS). The finite element method is used to discretize simultaneously the electrostatic and mechanical fields. The formulation is consistently derived from variational principles based on the electro-mechanical free energy. In classical weakly coupled formulations staggered iteration is used between the electro-static and the mechanical domain. Therefore, in those approaches, linear stiffness is evaluated by finite differences and equilibrium is reached typically by relaxation techniques. The strong coupling formulation presented here allows to derive exact tangent matrices of the electro-mechanical system. Thus it allows to compute non-linear equilibrium positions using Newton-Raphson type of iterations combined with adaptive meshing in case of large displacements. Furthermore, the tangent matrix obtained in the method exposed in this paper greatly simplifies the computation of vibration modes and frequencies of the coupled system around equilibrium configurations. The non-linear variation of frequencies with respect to voltage and stiffness can then be investigated until pull-in appears. In order to illustrate the effectiveness of the proposed formulation numerical results are shown first for the reference problem of a simple flexible capacitor, then for the model of a micro-bridge.
11 citations
TL;DR: In this article, the symmetry of the tangent operator for nonlinear shell theories with the finite rotation field was examined and it was shown that by adopting a rotation vector as a variable, the symmetry can be achieved in the Lagrangean description.
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.
10 citations
TL;DR: In this paper, a mixed finite element for the analysis of the Biot theory in saturated porous media is proposed. And the weak form of the governing equations of coupled hydro-dynamic problems within the element are given on the basis of the Hu-Washizu three-field variational principle.
Abstract: A mixed finite element for hydro-dynamic analysis in saturated porous media in the frame of the Biot theory is proposed. Displacements, effective stresses, strains for the solid phase and pressure, pressure gradients, and Darcy velocities for the fluid phase are interpolated as independent variables. The weak form of the governing equations of coupled hydro-dynamic problems in saturated porous media within the element are given on the basis of the Hu–Washizu three-field variational principle. In light of the stabilized one point quadrature super-convergent element developed in solid continuum, the interpolation approximation modes for the primary unknowns and their spatial derivatives of the solid and the fluid phases within the element are assumed independently. The proposed mixed finite element formulation is derived. The non-linear version of the element formulation is further derived with particular consideration of pressure-dependent non-associated plasticity. The return mapping algorithm for the integration of the rate constitutive equation, the consistent elastoplastic tangent modulus matrix and the element tangent stiffness matrix are developed. For geometrical non-linearity, the co-rotational formulation approach is used. Numerical results demonstrate the capability and the performance of the proposed element in modelling progressive failure characterized by strain localization due to strain softening in poroelastoplastic media subjected to dynamic loading at large strain. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: An advanced numerical formulation for the geometrically nonlinear finite element analysis of the shell structures under non-conservative loads is proposed in this paper, where the nonconservative follower loads are efficiently implemented by the load correction stiffness matrix (LCSM).
Abstract: An advanced numerical formulation for the geometrically nonlinear finite element analysis of the shell structures under nonconservative loads is proposed in the present paper. The nonconservative follower loads are efficiently implemented by the load correction stiffness matrix(LCSM). The implications and assumptions adopted to derive LCSM are thoroughly explored in this study to take reasonable approach for the problem. The formulations derived here can consider the loads applied to the arbitrary locations of the shell elements. The second order rotations are additionally incorporated into the displacement field of an element and the combined effect with the present nonconservative loads is included. It is demonstrated that the nonconservative loads and the improved displacement field all contribute to the tangent stiffness matrix, by which beneficial effects on the convergence behavior can be expected. In the companion paper, the present theory successfully finds its good and important application in the analysis of prestressed concrete shell structure under nonconservative loads. It will be seen in the companion paper that the proposed theory provides very efficient and accurate method for the realistic analysis of prestressed concrete shell structures under nonconservative follower loads.
TL;DR: In this article, a new method for modelling the stiffness of elastic body with viscoelastic theory is presented, and the parameters of the model set-up by using this method can be determined easily and present the characteristics of the elastic body's static stiffness, dynamic stiffness and shock stiffness.
TL;DR: In this article, a weighted residual formulation of equilibrium equations for nonlinear structural analysis is presented in material description, starting from the strong form, the weak form is derived by means of a suitable choice of weighting functions.
TL;DR: In this article, the implicit integration and consistent tangent modulus of a high-temperature constitutive model were derived in a general form by introducing a set of fourth-rank constitutive parameters into discretized kinematic hardening.
Abstract: This paper is concerned with the implicit integration and consistent tangent modulus of a high-temperature constitutive model, in which time-dependent inelastic strain rate consists of the transient part affected by kinematic and isotropic hardenings and the steady part depending on stress and temperature. Such a model is useful for high-temperature structure analysis and is practical because of the ease in determining material constants. The implicit integration is shown to result in two scalar-valued equations, and the consistent tangent modulus is derived in a general form by introducing a set of fourth-rank constitutive parameters into discretized kinematic hardening. The constitutive model is, then, implemented in a finite element program and applied to lead-free solder joint analysis. It is demonstrated that the implicit integration is very accurate if the kinematic hardening model of Ohno and Wang is employed, and that the consistent tangent modulus affords parabolic convergence to the Newton-Raphson iteration for solving nodal force equilibrium equations.
TL;DR: In this paper, a non-linear shear deformable shell element is presented for the solution of stability problems of stiffened plates and shells, which is exactly defined on the midsurface.
Abstract: The formulation of a non-linear shear deformable shell element is presented for the solution of stability problems of stiffened plates and shells. The formulation of the geometrical stiffness presented here is exactly defined on the midsurface and is efficient for analyzing stability problems of thick plates and shells by incorporating bending moment and transverse shear resultant force. As a result of the explicit integration of the tangent stiffness matrix, this formulation is computationally very efficient in incremental nonlinear analysis. The element is free of both membrane and shear locking behaviour by using the assumed strain method such that the element performs very well in the thin shells. By using six degrees of freedom per node, the present element can model stiffened plate and shell structures. The formulation includes large displacement effects and elasto-plastic material behaviour. The material is assumed to be isotropic and elasto-plastic obeying Von Mises`s yield condition and its associated flow rules. The results showed good agreement with references and computational efficiency.
TL;DR: Tangent Planes of a Quadratic Function: Tangent planes of a quadratic function as mentioned in this paper are a generalization of the tangent plane of a regular function, and they can be used to represent quadratics.
Abstract: (2003). Tangent Planes of a Quadratic Function. The College Mathematics Journal: Vol. 34, No. 3, pp. 205-206.
Journal Article•
TL;DR: Wang et al. as discussed by the authors proposed an FEM model for stiffness analysis of a light bus body, which was made in China, and the boundary condition of leaf spring and analysis load were discussed too.
Abstract: Structure analysis of light bus body usually just lays particular stress on intensity index and the experimental result of structure intensity is the key index of equipment registration in China. But, the body's structure stiffness also should be one of the key indexes. And, when the body's structure is design under stiffness criterion, it can satisfy the intensity criterion very well at the same time. The body's stiffness includes flexural stiffness and torsional stiffness. The flexural stiffness can be described as the body's deflection, under the plumb load, and the torsional stiffness can be described as the body's torsion angel, under the torsion load. A FEM model for stiffness analysis of a light bus body, which is made in China, is established in this paper. The FEM model's boundary condition--the supporting simulation of leaf spring, and analysis load--how to distribution the load to the FEM model are discussed too. Then, the FEM model is validated by experimental result. Moreover, by identifying the design variable, state variable, and the objective function of the model, the parts' sensitivity of body's flexural stiffness and torsional stiffness, which are constitutive parts of body frame or chassis, are analyzed respectively, using ANSYS. Choosing design variable due to the sensitivity analysis result, using the body's gross mass and the maximum stress of the parts as the state variable, and using the body's flexural stiffness and torsional stiffness as the objective function, the body's flexural stiffness and torsional stiffness are optimized.
Journal Article•
TL;DR: In this paper, the buckling properties of plates and shells were analyzed for element tangent stiffness matrix with consideration of material nonlinearity and geometrical non-linearity, and a penalty element was adopted to consider displacement restraint condition of loading boundary.
Abstract: The plates and shells are discreted by degenerated shell element with nine nodes and the buckling property and analyzed for element tangent stiffness matrix with consideration accorded material nonlinearity and geometrical nonlinearity. A penalty element is adopted to consider displacement restraint condition of loading boundary. Using the correlative program, buckling analysis was made with plates, shells and portal frame made of plates. The comparison indicates that the present theory and the suggested method has great accuracy and reliability.
TL;DR: A purely algebraic approach to higher order analysis of (singular) configurations of rigid multibody systems with kinematic loops (CMS) is presented in this article, where rigid body con.gurations are described by elements of the Lie group SE(3) and so the rigid body kinematics is determined by an analytical map f : V SE( 3), where V is the configuration space, an analytic variety.
Abstract: A purely algebraic approach to higher order analysis of (singular) configurations of rigid multibody systems with kinematic loops (CMS) is presented. Rigid body con.gurations are described by elements of the Lie group SE(3) and so the rigid body kinematics is determined by an analytical map f : V SE(3), where V is the configuration space, an analytic variety. Around regular configurations V has manifold structure but this is lost in singular points. In such points the concept of a tangent vector space does not makes sense but the tangent space CqV (a cone) to V can still be defined. This tangent cone can be determined algebraically using the special structure of the Lie algebra se (3), the generating algebra of the special Euclidean group SE (3), and the fact that the push forward map f*, the tangential mapping CqV se (3), is given in terms of the mechanisms screw system. Moreover the differentials of f of arbitrary order can be expressed algebraically. The tangent space to the configuration space can be shown to be a hypersurface of maximum degree 4, a vector space for regular points. It is the structure of the tangent cone to V that gives the complete geometric picture of the configuration space around a (singular) point. Identification of the screw system and its matrix representation with the kinematic basic functions of the CMS allows an automatic algebraic analysis of mechanisms.
TL;DR: In this paper, a kinematical approach based on the consideration of the contact conditions in the local coordinate system is proposed for the contact description and for consistent linearization, which leads to a simple structure of the tangent matrix, which is subdivided into main, rotational and curvature parts.
Abstract: A kinematical approach, based on the consideration of the contact conditions in the local coordinate system, is proposed for the contact description and for consistent linearization. This leads to a simple structure of the tangent matrix, which is subdivided into main, rotational and curvature parts. Various alternatives neglecting parts of the contact tangent matrix are considered. Representative examples show the effectiveness of the proposed approach for contact problems with arbitrary large deformation.