Showing papers on "Direct stiffness method published in 1985"

Stiffness matrix adjustment using mode data

Abstract: A procedure is introduced that uses, in addition to mode data, structural connectivity information to optimally adjust deficient stiffness matrices The adjustments performed are such that the percentage change to each stiffness coefficient is minimized The physical configuration of the analytical model is preserved and the adjusted model will exactly reproduce the modes used in the identification The theoretical development is presented and the procedure is demonstrated by numerical simulation of a test problem

A note on tangent stiffness for fully nonlinear contact problems

Abstract: SUMMARY In the numerical solution of geometrically nonlinear contact problems by the finite element method, it is often assumed that the modification to the tangent stiffness takes the form of the single rank-one-update characteristic of the linear theory. It is shown that due to the kinematic nonlinearity such a simple structure no longer holds. Within the context of the discrete problem arising from a finite element formulation, explicit expressions for the residual and the tangent stiffness matrix are obtained for both penalty and Lagrangian parameter procedures. FORMULATION OF THE DISCRETE PROBLEM By introducing the perturbed Lagrangian functional, both penalty and Lagrange parameter procedures may be presented in a unified manner. For the discrete description of the contact problem, the perturbed Lagrangian function, re, may be expressed as

Beam element matrices derived from Vlasov's theory of open thin‐walled elastic beams

Abstract: A uniform beam element of open thin-walled cross-section is studied under stationary harmonic end excitation. An exact dynamic (transcendentally frequency-dependent) 14 × 14 element stiffness matrix is derived from Vlasov's coupled differential equations. Special attention is paid to the computational problems arising when coefficients vanish in these equations because of symmetric cross-section, zero warping stiffness, etc. The dynamic element stiffness matrix is established via a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices. A static stiffness matrix is also derived and the associated consistent mass and geometric stiffness matrices are given. Modal masses are evaluated. A FORTRAN program and a numerical example are included.

Partitioned Runge-Kutta methods with stiffness detection and stepsize control

Abstract: For the numerical solution of autonomous initial value problems partitioned Runge-Kutta methods are studied, consisting of anA-stable Rosenbrock-Wanner method for the treatment of the stiff components and a customary Runge-Kutta method for the nonstiff part. The equations of condition including the coupling conditions are presented. An automatic stiffness detection and a stepsize control for two different algorithms are developed. The first algorithm PRK4 of order (3)4 possesses an automatic componentwise stiffness detection. The second algorithm RKF4RW treats the whole system as nonstiff or as stiff. RKF4RW is based on the well-known Runge-Kutta-Fehlberg pair of order 4(5). Additionally a ROW method of order (3)4 with anA-stable fourth order approximation is embedded. Usually RKF4RW is the faster algorithm and the system stiffness detection works more reliable than the componentwise stiffness detection in PRK4.

New Finite Element for Bond‐Slip Analysis

Abstract: A new finite element for bond stress‐slip analysis is presented. A one dimensional model which is based on equilibrium and local bond stressslip law is developed. The relationship between axial force and slip at the elements nodes is expressed through a stiffness matrix. The global stiffness matrix is assembled and solution yields slip, strain and stress distributions along the steel bar. The nonlinear bond stress‐slip relationship leads to an iterative technique which is found to converge rapidly. The proposed method predictions are compared with experimental results of monotonic and push‐pull tests and very good correspondence is found.

Geometrical analysis of compliant mechanisms in robotics (euclidean group, elastic systems, generalized springs

Abstract: The coordinate free approach to compliant mechanisms in robotics is developed It is shown that there is no natural positive definite metric on the group SE(3) of rigid body motions and that SE(3) supports a natural family of hyperbolic metrics Classification of subgroups of SE(3) is used to classify invariant constraints which include lower pairs of mechanism theory as a special case Stiffness of a generalized spring is intrinsically defined It is shown that a generic spring stiffness matrix has a normal form which maximally decouples rotational and translational aspects of stiffness Center of stiffness is defined as the origin of the coordinate frame in which the stiffness matrix assumes this normal form Analogous results hold for compliance instead of stiffness Construction of an arbitrary generalized spring by using only stable line springs is described Elastic systems are defined and their stiffness derived Equilibrium of an elastic system and its stability are discussed Holonomic constraints are introduced as limits of very stiff springs Elastic system with constraints is explicitly described in terms of the Grassmannian formalism Such systems are shown to be characterized by Lagrangian planes which are naturally reciprocal Remote center of compliance device, force sensing, and constrained motion are discussed as examples

Parametric Stiffness Control of Flexible Structures

Abstract: An unconventional method for control of flexible space structures using feedback control of certain elements of the stiffness matrix is discussed. The advantage of using this method of configuration control is that it can be accomplished in practical structures by changing the initial stress state in the structure. The initial stress state can be controlled hydraulically or by cables. The method leads, however, to nonlinear control equations. In particular, a long slender truss structure under cable induced initial compression is examined. both analytical and numerical analyses are presented. Nonlinear analysis using center manifold theory and normal form theory is used to determine criteria on the nonlinear control gains for stable or unstable operation. The analysis is made possible by the use of the exact computer algebra system MACSYMA.

Sparse matrix factor modification in structural reanalysis

Abstract: Structural reanalysis problems, such as in nonlinear finite element analysis or optimum design, involve progressive changes in the global stiffness matrix and its matrix factors. Although many studies have been devoted to the subject of matrix factor modification, most investigations have dealt with the problem separately from sparse matrix methods. This paper introduces a graph-theoretic model for the forward solution procedure which is applicable for identifying the modified entries of the matrix factors due to changes in the original matrix. Applications of this graph-theoretic model to existing refactorization methods are presented. The relation between substructuring and sparse matrix ordering strategies, and their effects on reanalysis are discussed. Modification of a sparse matrix associated with an n × n finite element grid ordered by the nested dissection scheme is analysed.

Computer Analysis of Structures: Matrix Structural Analysis Structured Programming

Abstract: 1. Mathematical Models of Elements. 2. Preparation for Matrix Displacement Method. 3. Matrix Displacement Method: Plane Structures. 4. Matrix Displacement Method: Special Topics. 5. Matrix Displacement Method: Space Structures. 6. Solution of System Equations. 7. Program Development. Appendices: Element Actions and Responses. Slope-Deflection Method. Coordinate Transformations. Principles and Concepts of Analytical Mechanics. Imposition of Constraints on System Model.

Probabilistic finite elements for transient analysis in nonlinear continua

Abstract: The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Stiffness control of large space structures

Abstract: A technique for using internal force producing dual element/actuators for vibration suppression of large space structures is proposed The method is applied to a low order system Selective modal damping is achieved The actuators used in this method may be electrically powered The method is suitable for structures which are too slender or flimsy to permit the use of reaction jet-type actuators

The condensation of the boundary element stiffness matrix in FEBEM analysis

Abstract: Two alternatives are discussed to take into consideration symmetry due to shape and loading in the development of the boundary element stiffness matrix. The resulting boundary element stiffness matrix is coupled with the finite element stiffness matrix and the displacements are computed for a circular tunnel. There is a considerable saving in computation time when symmetry is considered by either of the alternatives, but one appears to be preferable to the other.

Condensation of elastic half space soil stiffness matrix considering symmetry

Abstract: The finite element formulation for deriving the soil stiffness matrix by idealizing the foundation as an elastic half space is presented. The procedure for condensation of the soil stiffness matrix taking symmetry into consideration is discussed. Computation time is considerable reduced when a condensed soil stiffness matrix is used for the finite element analysis of rafts resting on an elastic half space.

Finite control volume method as applied to a slider bearing with side‐leakage

Abstract: The Reynolds' equation, which governs the pressure distribution in the oil film of a lubricated bearing, has been solved numerically using finite difference and finite element methods. The latter depends on finding the integral formulation of the Reynold's equation, which is minimized to determine the pressure distribution. The finite control volume method uses the basic flow equations, assumes a given interpolation function for the pressure and, by considering the net flow towards each nodal point, the geometry stiffness is obtained which is identical to the element stiffness matrix obtained by the classical finite element approach. The motivation of the finite control volume method (FCVM) lies in the fact that the calculus of variation, a stumbling block for solution of certain flow problems, is not considered.

'sore-plus' an out of core skyline solution routine.

Abstract: This paper is concerned with the solution of large systems of equations with mixed variables. That is, in the stiffness method of structural analysis, both nodal displacements and forces are unknowns. From this it is also able to perform static condensation of a stiffness matrix without reordering the node-numbers of the system of equations, and thus the skyline profile is preserved. The utility routines associated with the formation of the stiffness matrix as well as the solution algorithm itself are given, in the Appendix.

Microcomputer-aided structural analysis

Abstract: The recent expansion in computer power available with microcomputers has yet to be fully utilized by the structural engineer for teaching or production. A package of microcomputer based structural analysis programs called SAM (Structural Analysis by Microcomputer) is presented. A review of the direct stiffness method of structural analysis and a description of SAM demonstrates its advantages.

On the Consideration of Local Effects in the Finite Element Analysis of Large Structures

Abstract: Publisher Summary The finite element method is the most used tool for structural analysis during the design process. The main problem to the user is to set up a mesh that is fine enough for carrying out the stress distribution even in small regions of the structure. This chapter presents the finite element model of a car body. The model consists of 15000 degrees of freedom, and it is suitable for calculating the overall stiffness; however, it cannot consider the stress distribution. The number of the degrees of freedom must be increased to be able to work out a reliable stiffness distribution. In most cases, it is not possible because of the effort of the calculation. The chapter presents an iteration procedure that allows obtaining the solution of a locally refined system. The effort of the calculation depends on the size of the refined region, no matter how big the structure is; thereby local stress distribution can be worked out economically even for large structures. The algorithm is a combination of an iteration procedure with a direct solution.

Dynamic stiffness under rigid rectangular foundations resting on an elastic two-layered medium

Abstract: This paper deals with the dynamic stiffness (i. e., the complex stiffness) under rigid rectangular foundations resting on an elastic two-layered medium. This is a problem belonging to mixed boundary value problems which are not easily solved by an analytical approach. To overcome the difficulties of analysis the authors employ a numerical method, in which the contact area of the foundation is divided into a finite number of rectangular sub-regions, and a system of linear simultaneous equations with respect to the unknown contact pressures is derived by introducing the influence functions. In this paper the authors mainly investigate the effects of the layering on the dynamic stiffness and the difference in the dynamic stiffness between the relaxed and welded boundary conditions on the contact plane.