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Showing papers on "Direct stiffness method published in 1995"


Journal ArticleDOI
TL;DR: In this paper, a technique is presented for the identification of localized reductions in the stiffness of a structure using natural frequency measurements, which minimizes one of three criteria: (1) the changes in the element stiffnesses; (2) the norm of the changes to the global stiffness matrix; or (3) the residuals of the eigenvalue problem.
Abstract: A technique is presented for the identification of localized reductions in the stiffness of a structure using natural frequency measurements. The sensitivities of the eigenvalues to localized changes in the stiffness have been developed as a set of underdetermined equations. These equations have been used as the constraints in an optimization problem, which minimizes one of three criteria: (1) the changes in the element stiffnesses; (2) the norm of the changes to the global stiffness matrix; or (3) the residuals of the eigenvalue problem. An additional constraint, which forces the stiffness to always decrease due to damage, places the optimization problem in the realm of nonlinear programming. The overall formulation has provided a useful method to identify damage with a small number of measured natural frequencies. Ten to 90% localized reduction in stiffness was successfully identified in a 10-story, two-bay steel frame. The method was verified using test data from an aluminum, cantilever beam.

143 citations


Journal ArticleDOI
TL;DR: In this article, an exact stiffness matrix method is presented to evaluate the dynamic response of a multi-layered poroelastic medium due to time-harmonic loads and fluid sources applied in the interior of the layered medium.
Abstract: An exact stiffness matrix method is presented to evaluate the dynamic response of a multi-layered poroelastic medium due to time-harmonic loads and fluid sources applied in the interior of the layered medium. The system under consideration consists of N layers of different properties and thickness overlying a homogeneous half-plane or a rigid base. Fourier integral transform is used with respect to the x-co-ordinate and the formulation is presented in the frequency domain. Fourier transforms of average displacements of the solid matrix and pore pressure at layer interfaces are considered as the basic unknowns. Exact stiffness (impedance) matrices describing the relationship between generalized displacement and force vectors of a layer of finite thickness and a half-plane are derived explicitly in the Fourier-frequency space by using rigorous analytical solutions for Biot's elastodynamic theory for porous media. The global stiffness matrix and the force vector of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces. The numerical solution of the global equation system for discrete values of Fourier transform parameter together with the application of numerical quadrature to evaluate inverse Fourier transform integrals yield the solutions for poroelastic fields. Numerical results for displacements and stresses of a few layered systems and vertical impedance of a rigid strip bonded to layered poroelastic media are presented. The advantages of the present method when compared to existing approximate stiffness methods and other methods based on the determination of layer arbitrary coefficients are discussed.

101 citations


Journal ArticleDOI
TL;DR: In this article, the exact vibration frequencies of generally laminated beams are found using a new method, including the effect of rotary inertia and shear deformations. But this method is not suitable for rigid structures.

96 citations


Journal ArticleDOI
TL;DR: In this article, the linear flexural stiffness, incremental stiffness, mass, and consistent force matrices for a simple two-node Timoshenko beam element are developed based upon Hamilton's principle, where interdependent cubic and quadratic polynomials are used for the transverse and rotational displacements, respectively.

89 citations


Journal ArticleDOI
TL;DR: In this article, a non-linear formulation of the second-order terms in the strain-displacement relationship is proposed to represent axial displacement along the deformed (instead of undeformed) axis.
Abstract: In this paper, the equations of motion of flexible multibody systems are derived using a nonlinear formulation which retains the second-order terms in the strain-displacement relationship. The strain energy function used in this investigation leads to the definition of three stiffness matrices and a vector of nonlinear elastic forces. The first matrix is the constant conventional stiffness matrix, the second one is the first-order geometric stiffness matrix ; and the third is a second-order stiffness matrix. It is demonstrated in this investigation that accurate representation of the axial displacement due to the foreshortening effect requires the use of large number or special axial shape functions if the nonlinear stiffness matrices are used. An alternative solution to this problem, however, is to write the equations of motion in terms of the axial coordinate along the deformed (instead of undeformed) axis. The use of this representation yields a constant stiffness matrix even if higher order terms are retained in the strain energy expression. The numerical results presented in this paper demonstrate that the proposed new approach is nearly as computationally efficient as the linear formulation. Furthermore, the proposed formulation takes into consideration the effect of all the geometric elastic nonlinearities on the bending displacement without the need to include high frequency axial modes of vibration.

87 citations


Journal ArticleDOI
TL;DR: In this article, an augmentation technique is proposed which takes into account micro-mechanical effects, and permits the symmetrization of the tangent stiffness during frictional slip phase.
Abstract: The detailed discretization of contact zones with contact stiffness based on real physical characteristics of contact surfaces can produce stiffness terms which induce ill-conditioning of the global stiffness matrix. Moreover the consistent treatment of frictional behaviour generates non-symmetric tangent stiffness matrices due to the non-associativity of the slip phase. Other non-symmetries are due to the coupling terms and to the dependencies on various parameters that can be involved. To overcome these difficulties almost consistent techniques based on two-step algorithms have been proposed in the past. Here an augmentation technique is proposed which takes into account micro-mechanical effects, and permits the symmetrization of the tangent stiffness during frictional slip phase.

82 citations


Journal ArticleDOI
TL;DR: In this paper, a method is presented to study the three-dimensional quasi-static response of a multi-layered poroelastic half-space with compressible constituents.

74 citations


Journal ArticleDOI
TL;DR: Based on a new generalized variational principle, a refined direct stiffness method (RDSM) which can be directly used to improve non-conforming elements is proposed in this paper, but the constraint condition of interelement continuity is satisfied in an average sense and as a result convergence and high accuracy are insured.
Abstract: Based on a new generalized variational principle, a refined direct stiffness method (RDSM) which can be directly used to improve non-conforming elements is proposed The formulation is similar to that of the direct stiffness method (DSM), but the constraint condition of interelement continuity is satisfied in an average sense and as a result convergence and high accuracy are insured The well-known BCIZ nine-parameter triangular thin plate bending element is refined by the RDSM to yield a new nine-parameter thin plate bending element RT 9 Numerical examples are presented to show that the present model passes the patch test and possesses high accuracy

61 citations


Journal ArticleDOI
TL;DR: In this article, a new method for determining mass and stiffness matrices from modal test data is presented, based on the identified modes and the mass-normalized mode shapes at the sensor locations and is not limited by either the number of driving points or measurement points.
Abstract: A new method for determining mass and stiffness matrices from modal test data is presented. The method builds on the identified modes and the mass-normalized mode shapes at the sensor locations and is not limited by either the number of driving points or measurement points, and so it is applicable to most general test settings. A mixed coordinate basis is defined for the mass and stiffness matrices which is analogous to the Craig-Bampton component mode synthesis method for finite element models. The resultant mass and stiffness are of minimal order necessary to span the measured modes, and the resulting generalized coordinates provide an objective basis for the test-derived matrices to be used as if they are component mode-synthesized finite element matrices. Inclusion of rigid-body modes and the relationship of the new method to traditional physical parameter computations based on mobility curves is considered. Examples of the method as applied to numerical and experimental data are provided.

52 citations


Journal ArticleDOI
TL;DR: In this article, a method is developed to obtain exact solutions for first and second moments of displacements for statically determinate beams that have spatially random stiffness, based on the full probabilistic characterization of the random stiffness so that the solutions are valid for any value of the coefficient of variation of the stiffness.

50 citations


Journal ArticleDOI
TL;DR: In this article, a method to predict structural damage in its location and severity from modal characteristics of the damaged structure is proposed, which is based on the geometry of the structure which is reflected in its mass and stiffness distribution.
Abstract: A method to predict structural damage in its location and severity from modal characteristics of the damaged structure is proposed. No a priori knowledge of the modal characteristics of a corresponding baseline structure is required in the proposed formulation. Instead, information on the geometry of the structure which is reflected in its mass and stiffness distribution is needed. From matrix structural analysis, a system of equations is generated which relates the relative change of stiffness of structural members to a load vector generated from modal parameters of the damaged structure. Different solution techniques are suggested to determine the damage from the generated equations. The feasibility of the proposed formulation is demonstrated via a numerical example of a 10-storey building. Further, an error investigation on the error in the damage predictions due to uncertainties in the input data is carried out.

Journal ArticleDOI
TL;DR: Improved first-order approximations of displacements, stresses, and forces are presented to preserve the ease of implementation and the efficiency and to improve significantly the quality of the results, such that the method can be used in problems with very large changes in the design variables, including geometric changes and elimination of members.
Abstract: Improved first-order approximations of displacements, stresses, and forces are presented The main objectives in developing the method presented are 1) to preserve the ease of implementation and the efficiency of the common first-order approximations and 2) to improve significantly the quality of the results, such that the method can be used in problems with very large changes in the design variables, including geometrical changes and elimination of members The method is based on results of a single exact analysis and can be used with a general finite element system It is suitable for different types of design variables and structures Results obtained by the proposed method are compared with various first-order approximations for modifications in the cross section as well as the geometry and the topology of the structure It is shown that the proposed approximations are most effective in terms of the accuracy, the efficiency, and the ease of implementation

Journal ArticleDOI
TL;DR: It is shown that, at a central configuration, the stiffness matrix of the minimanipulator can be decoupled (diagona-lized), if proper design parameters are chosen.
Abstract: The dimensionally uniform Jacobian matrix of a novel three-limbed, six degree-of-freedom (DOF) minimanipulator is used to derive its dimensionally uniform stiffness matrix. The minimanipulator limbs are inextensible and its actuators are base-mounted. The lower ends of the limbs are connected to bidirectional linear stepper motors that are constrained to move on a base plane. The minimanipulator is capable of providing high positional resolution and high stiffness. It is shown that, at a central configuration, the stiffness matrix of the minimanipulator can be decoupled (diagona-lized), if proper design parameters are chosen. It is also shown that the stiffness of the minimanipulator is higher than that of the Stewart platform. Guidelines for obtaining large minimanipulator stiffness values are established. © 1995 John Wiley & Sons, Inc.

Journal ArticleDOI
TL;DR: In this paper, a general procedure for incorporating the effects of joint flexibility into standard methods for the analysis of frames is presented, which can allow for joint flexibility associated with all six degrees of freedom normally considered when analysing three-dimensional frames, including coupling between deformations.

Journal ArticleDOI
TL;DR: In this paper, a formulation for the plane 4-node quadrilateral finite element based on the principle of virtual displacements for a deformable body is developed, which is suitable for nonlinear analysis.
Abstract: A formulation for the plane 4-node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body. Incompatible modes are added to the standard displacement field. Then expressions for gradient operators are obtained from an expansion of the basis functions into a second-order Taylor series in the physical co-ordinates. The internal degrees of freedom of the incompatible modes are eliminated on the element level. A modified change of variables is used to integrate the element matrices. For a linear elastic material, the element stiffness matrix can be separated into two parts. These are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix. The formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials. Further, the approach is suitable for non-linear analysis. There, an application is given for the calculation of inelastic problems in physically non-linear elasticity. The element is efficient to implement and it is frame invariant. Locking effects and zero-energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion. A high accuracy is obtained for numerical solutions in displacements and stresses.

Journal ArticleDOI
TL;DR: In this article, an exact stiffness analysis of thick beams is presented based on a higher-order shear deformation theory, which leads to an element stiffness matrix that is an extension of the standard matrix based on classical beam theory.

Journal ArticleDOI
TL;DR: In this paper, a dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations, which eliminates spatial discretization error and is capable of predicting many natural modes with use of a small number of degrees of freedom.

Journal ArticleDOI
TL;DR: In this article, a dynamic stiffness matrix is formed by frequency-dependent shape functions which are exact solutions of the governing differential equations of a non-uniform column and the natural frequencies of the nonuniform beams under axial force can be found by equating to zero the determinant of the dynamic stiffness matrices of the system.

Journal ArticleDOI
TL;DR: In this article, an exact and direct modeling technique is presented for modeling beam structures based on the combination of transfer and dynamic stiffness matrices, which can predict accurately all the eigensolutions in a large frequency range in terms of a low dimension dynamic stiffness matrix.

Journal ArticleDOI
TL;DR: In this paper, the general non-symmetric parametric form of the incremental secant stiffness matrix for non-linear analysis of solids using the finite element metod is derived.
Abstract: In this paper the general non symmetric parametric form of the incremental secant stiffness matrix for non linear analysis of solids using the finite element metod is derived. A convenient symmetric expression for a particular value of the parameters is obtained. The geometrically non linear formulation is based on a Generalized Lagrangian approach. Detailed expressions of all the relevant matrices involved in the analysis of 3D solids are obtained. The possibilities of application of the secant stiffness matrix for non linear structural problems including stability, bifurcation and limit load analysis are also discussed. Examples of application are given for the non linear analysis of pin joined frames.

Journal ArticleDOI
TL;DR: In this paper, the stiffness matrix for a curved beam element can be used in analyzing the behavior of horizontally curved bridges for either open or closed sections, and the results of the solution are compared with another study using a closed form solution.

Journal ArticleDOI
TL;DR: In this article, a simple contact-friction interface element for two-dimensional models is developed, which can simulate frictional slippage, decoupling and re-bonding of two bodies initially mating at a common interface.

Journal ArticleDOI
TL;DR: In this article, the exact vibration frequencies of multi-span laminated beams are found using the exact element method, including the effect of rotary inertia and shear deformations.

Journal ArticleDOI
TL;DR: In this article, a theoretical background and computation algorithms of equilibrium finite element method are presented there, and different external effects are estimated, namely: load, prestressing, inicial strains and support settlements.
Abstract: Summary A problem of elastic structures stress-strain field determination is considered in this article. A theoretical background and computation algorithms of equilibrium finite element method are presented there. The different external effects are estimated, namely: load, prestressing, inicial strains and support settlements. The dual relationships (equilibrium and geometrical equations, stiffness and flexibility equations) of equilibrium element, also the expressions of stiffness and flexibility matrices are given. These relationships describe the stress-strain field of the finite element and allow to transforme the flexibility matrix to the stiffness matrix and on the contrary. There are presented direct and variational formulations of the problem. The algorithms of the forces method and displacements method are made for their solution. Easier is the algorithm of displacements method, because making equations of the forces method needs to solve the system of equilibrium equations. But the formulation ...

Journal ArticleDOI
TL;DR: In this article, the concept and techniques from the field of Parametrized Variational Principles (PVPs) are extended to Matrix Structural Analysis (MSA), where free parameters are used as weighting factors of governing discrete equations.

Journal ArticleDOI
TL;DR: In this article, a computer program developed by the authors, for design-office use, where the matrix stiffness method has been adjusted to incorporate all these non-linearities is described.

Journal ArticleDOI
TL;DR: The theoretical foundations and principles governing the design of the test fixtures, including the load frame, for use in conjunction with the direct complex stiffness test method for the characterization of the dynamic properties of viscoelastic elements are presented in this paper.

Journal ArticleDOI
TL;DR: In this paper, a symbolic algebra package, Mathematica, is used to investigate the analytical integration of the mixed finite element stiffness matrices, which can be applied to general two and three-dimensional mixed finite elements with careful simplification of integrands to avoid excessive growth in the symbolic expressions.

Proceedings ArticleDOI
05 Aug 1995
TL;DR: The theory suggests that it is possible to introduce a nonsymmetric stiffness matrix in robotic control so as to have energy dissipation (damping) effects, which is useful when passive damping effects are desirable in grasping.
Abstract: In this paper, we present fundamental properties of stiffness matrix as applied to analysis of grasping and dextrous manipulation. The investigation unveils insights of stiffness matrix which are important in grasping and manipulation for robotic hands and fingers in R/sup 3/ space. A general grasp stiffness matrix can be broken into two parts-symmetric and antisymmetric. The symmetric part is derived from a conservative quadratic potential function in the Hermitian form; while the antisymmetric part is a function of nonconservative curl vector field of the grasp. The conservative part stores and interchanges energy with the environment with which the fingers make contact. The nonconservative part dissipates or increases energy. The theory suggests that it is possible to introduce a nonsymmetric stiffness matrix in robotic control so as to have energy dissipation (damping) effects. This is useful when passive damping effects are desirable in grasping. Application of the theory to the analysis of stiffness matrix in 3D is presented for analysis of grasping and manipulation.

Journal ArticleDOI
TL;DR: In this article, a spanning set of orthonormalized stress modes can be generated to simplify the matrix equations and allow explicit expressions for element stiffness coefficients to be derived, and the developed methodology is demonstrated using several selected 2-D quadrilateral and 3-D hexahedral elements.
Abstract: The hybrid stress method has demonstrated many improvements over conventional displacement-based formulations. A main detraction from the method, however, has been the higher computatational cost in forming element stiffness coefficients due to matrix inversions and manipulations as required by the technique. By utilizing permissible field transformations of initially assumed stresses, a spanning set of orthonormalized stress modes can be generated which simplify the matrix equations and allow explicit expressions for element stiffness coefficients to be derived. The developed methodology is demonstrated using several selected 2-D quadrilateral and 3-D hexahedral elements.