Showing papers on "Tangent stiffness matrix published in 2009"
TL;DR: In this article, the authors present an efficient computer method for inelastic and large deflection analysis of steel space frames with non-linear flexible joint connections, based on the most refined type of second-order analysis, the plastic zone analysis.
51 citations
TL;DR: A computationally efficient formulation and an algorithm for tetrahedral finite-element simulation of elastic objects subject to Saint Venant-Kirchhoff (StVK) material law are described.
Abstract: This article describes a computationally efficient formulation and an algorithm for tetrahedral finite-element simulation of elastic objects subject to Saint Venant-Kirchhoff (StVK) material law. The number of floating point operations required by the algorithm is in the range of 15p to 27p for computing the vertex forces from a given set of vertex positions, and 27p to 38p for the tangent stiffness matrix, in comparison to a well-optimized algorithm directly derived from the conventional Total Lagrangian formulation. In the new algorithm, the data is associated with edges and tetrahedron-sharing edge-pairs (TSEPs), as opposed to tetrahedra, to avoid redundant computation. Another characteristic of the presented formulation is that it reduces to that of a spring-network model by simply ignoring all the TSEPs. The technique is demonstrated through an interactive application involving haptic interaction, being combined with a linearized implicit integration technique employing a preconditioned conjugate gradient method.
50 citations
TL;DR: In this article, a linearized frequency domain analysis of a tension leg platform is presented, where the nonlinear restoring function and tangent stiffness matrix are derived and extensive nonlinear couplings between the different modes are found to exist.
47 citations
TL;DR: In this paper, the second-order work criterion is extended to quasi-static boundary-value problems by considering the stiffness matrix arising from finite element discretization, and the importance of the first vanishing eigenvector associated with the symmetrical part of the stiffness matrices is discussed.
Abstract: The present paper investigates bifurcation analysis based on the second-order work criterion, in the framework of rate-independent constitutive models and rate-independent boundary-value problems. The approach applies mainly to nonassociated materials such as soils, rocks, and concretes. The bifurcation analysis usually performed at the material point level is extended to quasi-static boundary-value problems, by considering the stiffness matrix arising from finite element discretization. Lyapunov's definition of stability (Annales de la faculte des sciences de Toulouse 1907; 9:203-274), as well as definitions of bifurcation criteria (Rice's localization criterion (Theoretical and Applied Mechanics. Fourteenth IUTAM Congress, Amsterdam, 1976; 207-220) and the plasticity limit criterion are revived in order to clarify the application field of the second-order work criterion and to contrast these criteria. The first part of this paper analyses the second-order work criterion at the material point level. The bifurcation domain is presented in the 3D stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. The relevance of this criterion, when the nonlinear constitutive model is expressed in the classical form or in the dual form, is discussed. In the second part, the analysis is extended to the boundary-value problems in quasi-static conditions. Nonlinear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples, the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode in the homogeneous and nonhomogeneous boundary-value problem.
44 citations
TL;DR: In this article, a time-integration algorithm for solving a non-linear viscoelastic-viscoplastic (VE-VP) constitutive equation of isotropic polymers is presented.
Abstract: The present study introduces a time-integration algorithm for solving a non-linear viscoelastic–viscoplastic (VE–VP) constitutive equation of isotropic polymers. The material parameters in the constitutive models are stress dependent. The algorithm is derived based on an implicit time-integration method (Computational Inelasticity. Springer: New York, 1998) within a general displacement-based finite element (FE) analysis and suitable for small deformation gradient problems. Schapery's integral model is used for the VE responses, while the VP component follows the Perzyna model having an overstress function. A recursive-iterative method (Int. J. Numer. Meth. Engng 2004; 59:25–45) is employed and modified to solve the VE–VP constitutive equation. An iterative procedure with predictor–corrector steps is added to the recursive integration method. A residual vector is defined for the incremental total strain and the magnitude of the incremental VP strain. A consistent tangent stiffness matrix, as previously discussed in Ju (J. Eng. Mech. 1990; 116:1764–1779) and Simo and Hughes (Computational Inelasticity. Springer: New York, 1998), is also formulated to improve convergence and avoid divergence. Available experimental data on time-dependent and inelastic responses of high-density polyethylene are used to verify the current numerical algorithm. The time-integration scheme is examined in terms of its computational efficiency and accuracy. Numerical FE analyses of microstructural responses of polyethylene reinforced with elastic particle are also presented. Copyright © 2009 John Wiley & Sons, Ltd.
42 citations
TL;DR: In this paper, the stiffness matrix is expressed in terms of the screw coordinates with respect to the basis consisting of its eigenvectors, and the synthesis equation is derived, which allows one to select the positions or directions of the springs from the screw system spanned by the induced wrenches of the given stiffness matrix.
Abstract: It is possible to realize the desired compliance characteristics of a robot in a form of a passive compliance device, which demands the synthesis technique of a stiffness matrix by parallel connections of line and/or torsional springs. In this paper, the stiffness matrix is expressed in terms of the screw coordinates with respect to the basis consisting of its eigenvectors, thereby the synthesis equation is derived. Examination of the numbers of free design parameters involved in the synthesis suggests that a line or free vector for a spring can be freely selected from the induced wrench space depending on the rank of the stiffness matrix. The recursive synthesis method that allows one to select the positions or directions of the springs from the screw system spanned by the induced wrenches of the given stiffness matrix is proposed.
31 citations
TL;DR: In this article, a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is proposed, and two practical situations are examined, where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties.
Abstract: The recently developed short-time linear response algorithm, which predicts the response of a nonlinear chaotic forced-dissipative system to small external perturbation, yields high precision of the response prediction. However, the computation of the short-time linear response formula with the full rank tangent map can be expensive. Here, a numerical method to potentially overcome the increasing numerical complexity for large scale models with many variables by using the reduced-rank tangent map in the computation is proposed. The conditions for which the short-time linear response approximation with the reduced-rank tangent map is valid are established, and two practical situations are examined, where the response to small external perturbations is predicted for nonlinear chaotic forced-dissipative systems with different dynamical properties.
31 citations
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 coupling procedure based on the sequential iterative Dirichlet-Neumann coupling algorithm is presented, which utilizes the condensed tangent stiffness matrices at the soil-structure interface to ensure and accelerate convergence to compatibility in successive update of the boundary conditions.
25 citations
TL;DR: In this paper, the authors presented a new methodology that is more straightforward and simpler than existing techniques for computing the tangent stiffness matrix of a multi-degree-of-freedom (dof) test specimen.
Abstract: Researchers have long recognized the importance and potential benefits of utilizing the tangent stiffness matrix of a test specimen in hybrid simulations employing implicit and mixed-integration schemes. However, the computation of the tangent stiffness matrix during testing has proved to be challenging, particularly for test specimens with more than one degree of freedom (dof). This paper presents a new methodology that is more straightforward and simpler than existing techniques for computing the tangent stiffness matrix of a multi-dof test specimen. The proposed method is combined with the operator-splitting method (OSM), and the capabilities, advantages and limitations of the new formulation are demonstrated through several examples. The accuracy, stability, and error propagation characteristics of the modified OSM are also studied theoretically as well as numerically. The research results show that the proposed algorithm provides results that are better than those produced via the regular OSM alone, especially for damped structures undergoing highly inelastic behavior during testing.
24 citations
TL;DR: Cai et al. as mentioned in this paper presented a simple finite element method, based on simple mechanics and physical clarity, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section.
Abstract: This paper presents a simple finite element method, based on simple mechanics and physical clarity, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section. A co-rotational reference frame, involving the axes of each finitely rotated beam finite-element, is used as the Updated Lagrangian reference frame for the respective element. A von Karman type nonlinear theory of deformation is employed in the co-rotational reference frame of each beam element, to account for bending, stretching, and torsion of each element. An assumed displacement approach is used to derive an explicit expression for the (12x12) symmetric tangent stiffness matrix of the beam element in the co-rotational reference frame. From the finite-displacement vector at each of the two nodes of the beam element, an explicit expression is derived for the matrix of finite rotation of the co-rotational reference frame from the globally-fixed Cartesian reference frame. Thus, this paper provides a text-book example of an explicit expression for the (12x12) symmetric tangent stiffness matrix of a finitely deforming beam element, which can be employed in very simple analyses of large deformations of space-frames. This paper is also a celebration of the genius of Theodore von Karman (original Hungarian name Szöllöskislaki Kármán Tódor) (1881-1963), who received the first U.S. National Medal of Science in 1963, and who first proposed a simple nonlinear theory of plates in 1910, the essential ideas of which theory are adopted in the present paper, for beams of arbitrary cross-sections, in co-rotational reference frames. The present methodologies can be extended to study the very large deformations of plates and shells as well. Metal plasticity may 1 Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Department of Geotechnical Engineering, Tongji University, Shanghai 200092, P.R.China. E-mail: yc_cai@163.net 2 Center for Aerospace Research & Education, University of California, Irvine 3 Lloyd’s Register Educational Trust (LRET) Center of Excellence, Pusan National University, Korea 118 Copyright © 2009 Tech Science Press CMES, vol.53, no.2, pp.117-145, 2009 also be included, through the method of plastic hinges, etc.
TL;DR: In this article, an adaptation of Nguyen's model for brittle materials to the case of ductile rupture is presented. But the authors focus their attention on the formulation of a consistent tangent stiffness matrix which is essential for the efficiency and convergence of the implementation within a finite element framework.
TL;DR: In this article, the authors develop alternative discrete analogues of tangent bundles, by extending tangent vectors to finite curve segments, one curve segment for each tangent vector, which are then used as phase spaces for discretizations of the variational principles of Lagrangian systems.
01 Jul 2009
TL;DR: In this paper, a non-linear force method is applied instead of geometrically nonlinear finite-element method (NFEM) to analyze the nonlinear behavior of pin-joint structures and the relationship between the equilibrium matrix in NFM and the tangent stiffness matrix in NFEM is discussed.
Abstract: This paper is mainly concerned with a new method that analyses the non-linear behaviour of pin-joint structures. Geometrically, non-linear force method (NFM), which is derived from the force method, is now applied instead of geometrically non-linear finite-element method (NFEM). Singular value decomposition operation of the equilibrium matrix is introduced into the calculation of the responses of structures. The relationships between the equilibrium matrix in NFM and the tangent stiffness matrix in NFEM are discussed. The Newton—Raphson method is used in NFM's iteration procedure and the arc-length incremental strategy is also introduced in post-buckling analysis. Two classical structures and an infinitesimal mechanism are used as illustrative examples.
TL;DR: Cai et al. as discussed by the authors presented a simple finite element method, based on assumed moments and rotations, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section.
Abstract: This paper presents a simple finite element method, based on assumed moments and rotations, for geometrically nonlinear large rotation analyses of space frames consisting of members of arbitrary cross-section. A von Karman type nonlinear theory of deformation is employed in the updated Lagrangian co-rotational reference frame of each beam element, to account for bending, stretching, and torsion of each element. The Reissner variational principle is used in the updated Lagrangian co-rotational reference frame, to derive an explicit expression for the (12x12) symmetric tangent stiffness matrix of the beam element in the co-rotational reference frame. The explicit expression for the finite rotation of the axes of the corotational reference frame, from the global Cartesian reference frame is derived from the finite displacement vectors of the 2 nodes of each finite element. Thus, the explicit expressions for the tangent stiffness matrix of each finite element of the beam, in the global Cartesian frame, can be seen to be derived as text-book examples of nonlinear analyses. When compared to the primal (displacement) approach wherein C1 continuous trial functions (for transverse displacements) over each element are neccessary, in the current approch the trial functions for the transverse bending moments and rotations are very simple, and can be assumed to be linear within each element. The present (12×12) symmetric tangent stiffness matrices of the beam, based on the Reissner variational principle and the von Karman type simplified rod theory, are much simpler than those of many others in the literature. The present approach does not involve such numerical procedures as selective reduced integration or suppression of attendant Kinematic modes. The present methodolo1 Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Department of Geotechnical Engineering, Tongji University, Shanghai 200092, P.R.China. E-mail: yc_cai@163.net 2 Center for Aerospace Research & Education, University of California, Irvine 3 Lloyd’s Register Educational Trust (LRET) Center of Excellence, Pusan National University, Korea 336 Copyright © 2009 Tech Science Press CMES, vol.54, no.3, pp.335-368, 2009 gies can be extended to study the very large deformations of plates and shells as well. Metal plasticity may also be included, through the method of plastic hinges, etc. This paper is a tribute to the collective genius of Theodore von Karman (18811963) and Eric Reissner (1913-1996).
TL;DR: In this article, the authors derived a generic stiffness matrix for steel members accounting for the combined influence of P-delta effects, member shear deformation, inelasticity, semi-rigid connection, and joint damage.
TL;DR: In this article, a variational multiscale formulation of the time-dependent Navier-Stokes equations in 3D is presented. Butler et al. proposed a consistent Newton-Schur (NS) solution approach, which increases computational efficiency and parallel scalability by implementing the tangent stiffness matrix in Schur complement form.
Abstract: In the following paper, we present a consistent Newton–Schur (NS) solution approach for variational multiscale formulations of the time-dependent Navier–Stokes equations in three dimensions. The main contributions of this work are a systematic study of the variational multiscale method for three-dimensional problems and an implementation of a consistent formulation suitable for large problems with high nonlinearity, unstructured meshes, and non-symmetric matrices. In addition to the quadratic convergence characteristics of a Newton–Raphson-based scheme, the NS approach increases computational efficiency and parallel scalability by implementing the tangent stiffness matrix in Schur complement form. As a result, more computations are performed at the element level. Using a variational multiscale framework, we construct a two-level approach to stabilizing the incompressible Navier–Stokes equations based on a coarse and fine-scale subproblem. We then derive the Schur complement form of the consistent tangent matrix. We demonstrate the performance of the method for a number of three-dimensional problems for Reynolds number up to 1000 including steady and time-dependent flows. Copyright © 2009 John Wiley & Sons, Ltd.
01 Jan 2009
TL;DR: In this article, the radial return method on Chaboche model is used to solve line contact problem with assumption of Coulomb's friction, and the authors show that the number of iteration of N-R method is higher in case of continuum tangent modulus and many times higher with use of modified N -R method, initial stiffness method.
Abstract: For the numerical solution of elasto-plastic problems with use of Newton-Raphson method in global equilibrium equation it is necessary to determine the tangent modulus in each integration point. To reach the parabolic convergence of Newton-Raphson method it is convenient to use so called algorithmic tangent modulus which is consistent with used integration scheme. For more simple models for example Chaboche combined hardening model it is possible to determine it in analytical way. In case of more robust macroscopic models it is in many cases necessary to use the approximation approach. This possibility is presented in this contribution for radial return method on Chaboche model. An example solved in software Ansys corresponds to line contact problem with assumption of Coulomb’s friction. The study shows at the end that the number of iteration of N-R method is higher in case of continuum tangent modulus and many times higher with use of modified N-R method, initial stiffness method.
TL;DR: In this article, the analytical stiffness equations of the 3-RPR planar parallel mechanism are derived based on the Conservative Congruence Transformation (CCT) stiffness matrix proposed in [1-3].
Abstract: The analytical stiffness equations of the 3-RPR planar parallel mechanism are derived in this paper based on the Conservative Congruence Transformation (CCT) stiffness matrix proposed in [1-3]. Stiffness maps of the 3-RPR mechanism are plotted in order to show the behaviour of the stiffness with and without external forces. The stiffness characteristics of the mechanism are analyzed and discussed in details. Numerical examples show that the stiffness in x and in y are well balanced, while the stiffness in tends to be lower.
TL;DR: Based on Kirchhoff assumptions and generalized conforming theory, new 4-node quadrilateral flat shell element and 3-node triangular flat shell elements are presented in this article, which have vertical rotational degrees of freedom, and translation displacement field and rotation displacement field are mutually independent.
TL;DR: This work considers the performance of Local Tangent Space Alignment (Zhang & Zha), one of several manifold learning algorithms, which have been proposed as a dimension reduction method, and derives the first performance bound that has been derived.
16 Dec 2009
TL;DR: This paper presents a method, called Parameter-Separation Method, for stiffness analysis of parallel mechanisms, which applies a special way to formulate dimensionally homogeneous Jacobian matrix with consideration of the input need, and comes up with 2 criteria to judge the stiffness of parallel mechanism.
Abstract: This paper presents a method, called Parameter-Separation Method, for stiffness analysis of parallel mechanisms. By treating the effect of different parameters (i.e. external force and torque, translational and rotational displacement) separately, the method produces 4 criteria of stiffness analysis. A further method based on the first method is proposed when we conduct stiffness analysis on some parallel mechanisms whose inputs are of the same unit. It applies a special way to formulate dimensionally homogeneous Jacobian matrix with consideration of the input need, and comes up with 2 criteria to judge the stiffness of parallel mechanisms. These two methods are explained in detail, and their effects and relationship are demonstrated by stiffness analysis of a 4RRR redundantly actuated parallel mechanism.
01 Jan 2009
TL;DR: An efficient One-Step inverse approach based on nodal tangent plane (NTP) is proposed to predict the optimum blank shapes and sizes and reasonable estimation of forming severity (i.e., thickness, strain distributions) from desired final workpieces as discussed by the authors.
Abstract: An efficient One-Step inverse approach (IA) based on nodal tangent plane (NTP) is proposed to predict the optimum blank shapes and sizes and reasonable estimation of forming severity (i.e., thickness, strain distributions) from desired final workpieces. According to the deformation theory of plasticity, Hill’s planar isotropic yield criteria and the principle of virtual work (PVW), the non-linear elasto-plastic finite element equilibrium equations are obtained, in which the simplified boundary force conditions are also implemented to simulate the effects of punch, die, blank-holder and draw-bead. For solving the non-linear problem, Newton-Raphson method is used. However, in traditional One-Step IA, the local element stiffness matrix is assembled in the global coordinate system where bad convergence is always a severe problem, especially when vertical or quasi-vertical walls happen. Fortunately, the NTP method provides a smart solution to enhance the convergence, where the ill-conditioned matrix is avoided by assembling the local element stiffness matrix to the tangent plane and to the normal of node. The developed algorithm is integrated into independently developed KMAS (KingMesh Analysis System) for sheet metal forming. To validate its efficiency and feasibility, it is applied to square cup deep drawing of Numisheet’93 and front fender forming of Numisheet’2002 by comparing with DynaForm based on incremental algorithm and traditional One-Step IA.Copyright © 2009 by ASME
Journal Article•
TL;DR: In this paper, the effect of parasitic stiffness equations and the accuracy of rotational stiffness equations of flexure hinges on the overall analytical stiffness equations were comprehensively studied by the orthographic experimental method.
Journal Article•
TL;DR: In this article, the stiffness of a 3-PRR planar parallel mechanism is analyzed and discussed in details according to the stiffness expressions and numerical examples, and the stiffness characteristics of the mechanism are analyzed.
Abstract: To reveal the stiffness behavior of a parallel mechanism with considering the effect of the change in geometry due to compliance caused by the external forces,the stiffness characteristics of 3-PRR planar parallel mechanism were studied systemically.The analytical expressions of stiffness of the mechanism were derived on the basis of conservative congruence transformation(CCT) stiffness matrix.Then,the stiffness mapping curves of the 3-PRR mechanism were given to show the change and behavior of the stiffness with and without external forces acted on the mechanism,thus comparing the different changes in the stiffness and how it changes.And the stiffness characteristics of the mechanism were analyzed and discussed in details according to the stiffness expressions and numerical examples.The results show that the stiffness of the 3-PRR mechanism is configuration dependent,and proportional to the actuating forces and joint stiffness.The stiffness correlates not only to the magnitude of external forces but also the direction in which the external force act upon.
Journal Article•
TL;DR: A unified corotational kinematics of deformable bar elements that can be represented as plane truss, spatial truss or 2D beam elements is presented in this article, which is based on the separation of the motion on deformationaland rigid body components.
Abstract: This article presents a unified corotational kinematics of deformable bar elements that can be represented as plane truss, spatial truss or 2D beam elements. The corotational kinematics is based on the separation of the motion on deformationaland rigid body components. For the case of translations and rotations, determined by a single angular parameter, the deformational motions are expressible in closed form. It is demonstrated that the determination of the deformational motions are based on a unique vectorial expression independent on the bar element used. In addition, the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms.
29 Apr 2009
TL;DR: In this paper, the second-order work criterion is used to investigate bifurcation in geomaterials with the help of the second order work criterion and the analysis is extended to boundary value problems in quasi-static conditions, by considering the finite element stiffness matrix.
Abstract: The present paper investigates bifurcation in geomaterials with the help of the second-order work criterion. The approach applies mainly to non associated materials such as soils. The analysis usually performed at the material point level is extended to quasi-static boundary value problems, by considering the finite element stiffness matrix. The first part of the paper reminds some results obtained at the material point level. The bifurcation domain is presented in the 3D principal stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. In the second part, the analysis is extended to boundary value problems in quasi-static conditions. Non-linear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode even for non homogeneous boundary value problems.
Journal Article•
TL;DR: In this article, the authors proposed a method for computing tangent curves for 2D vector fields based on piecewise linear variation over a triangle in 2D, where the critical points can be easily found by solving a simple linear system for each triangle.
Abstract: This paper presents the development of certain highly efficient and accurate method for computing tangent curves for two-dimensional vector fields. Unlike convention methods, such as Runge-Kutta, for computing tangent curves which produce only approximations, the method developed herein produces exact values on the tangent curves based on piecewise linear variation over a triangle in 2D. This new method assumes that the vector field is piecewise linearly defined over a triangle in 2D. It is also required to decompose the rectangular cell into two triangular cells. The critical points can be easily found by solving a simple linear system for each triangle. This method is to find exit points by producing a sequence of points on the curve with the computation of each subsequent point based on the previous. Because points on the tangent curves are calculated by the explicit solution for each triangle, this new method provides correct topologies in visualizing 2D vector fields.
10 Jun 2009
TL;DR: Numerical and hybrid simulation are used to demonstrate that the proposed algorithm provides an efficient method for full implementation of implicit numerical integration in hybrid simulations of complex nonlinear structures.
Abstract: A fully implicit iterative integration procedure is presented for hybrid simulation of the seismic response of structural systems. The advantage of this approach is that experimental elements can be introduced into a simulation using fully implicit integration algorithms designed for pure numerical simulations. The procedure utilizes the tangent stiffness matrices for both numerical and experimental substructures. The tangent stiffness matrix for experimental substructures is estimated using readily available experimental measurements and by classical diagonalization that reduces the number of unknowns in the matrix. In order to avoid physical application of the iterative displacements to experimental substructures, the restoring force of each actuator is estimated using polynomial interpolation and extrapolation of experimental measurements. Numerical and hybrid simulation are used to demonstrate that the proposed algorithm provides an efficient method for full implementation of implicit numerical integration in hybrid simulations of complex nonlinear structures.
Journal Article•
TL;DR: Based on the field consistency principle of co-rotational procedure, a simple tangent stiffness matrix for the 2D quadrilateral element under large rotation with small strain is proposed in this paper.
Abstract: Although there are a lot of research achivements for co-rotational procedure of a 2D quadrilateral element, most of these elements were based on geometric consisitency and produced a symmertric element tangential stiffness matrix.For elements of field consistency, there are less research works so far.Based on the field consistency principle of co-rotational procedure, a simple tangent stiffness matrix for the 2D quadrilateral element under large rotation with small strain is proposed in this paper.Comparied with the symmetric tangential stiffness matrix of geometric consistency, the element tangential stiffness matrix is asymmetric but less of computation.In nonlinear computation, this is positively meaningful as the round off errors accumulate with the increase of computation of element stiffness matriecs and consequently lead to the possibility of iteration disconvergence.In collaboration with the proposed asymmetric element stiffness matrix, an unified incremental iteration scheme of combining displacement increamental method and load increamental method is employed for the solution of resulting nonlinear FEM equations and following the procedure mentioned above and its corresponding formulation, a FORTRAN computer program, named NSAP, has been developed.Computations and analysis for plane beams and arches have verified the correctness of the element's formulation, the high efficency of the program and the strong nonlinear computation ability of the method.It is cable of analyzing nonlinear behavior of planar stress of beams and arches.Computations presented reflect preferably a comprehensive understanding of geometrical nonlinear characteristics of beams and arches, could be beneficial for the engineeing designers.