Showing papers on "Direct stiffness method published in 1977"
TL;DR: In this article, a variational formulation is given for the equations of motion for an unconstrained elastic body, and Hamilton's principle is used to derive the equation of motion and deformation of the body.
Abstract: A variational formulation is given for the equations of motion for an unconstrained elastic body, and Hamilton's principle is used to derive the equations of motion and deformation of the body. Finite-element approximations are developed for these dynamical equations with respect to a body axis system satisfying the mean axis conditions. The free-body influence matrix for the body then is developed in terms of the finite-element model parameters.
96 citations
TL;DR: In this article, an energy measure of discretization error was proposed for finite element mesh refinement in the analysis of structural continua, based on the strain energy contributions by the admissible displacement response modes of an element.
Abstract: This paper proposes an energy measure of discretization error and examines its use for finite element mesh refinement in the analysis of structural continua.
The measure is based on the strain energy contributions by the admissible displacement response modes of an element. An element energy differential is obtained by separating the energy contribution due to the higher displacement modes. This measure is suitable for use with all element types based on the direct stiffness method.
The paper presents results of membrane, plate and shell analyses using the measure. It compares sequences of analysis with successively improved meshes to explore the quality of the measure. It concludes that the element energy difference provides a quantitative measure of the efficiency of a given mesh and a qualitative measure which is useful for selecting further mesh refinements, when necessary.
80 citations
TL;DR: In this article, a straightforward criterion to warrant the displacement functions being used in the finite element approximation of circular arches was established by studying the natural shape function, i.e. the exact solution of the deformed shape, of the circular arch element.
Abstract: This paper proposes a straightforward criterion to warrant the displacement functions being used in the finite element approximation of circular arches. The criterion was established by studying the natural shape function, i.e. the exact solution of the deformed shape, of the circular arch element. The exact stiffness matrix [K]exact is derived from the natural shape and is confirmed to be the inverse of the well-known flexibility matrix [F]exact in the curved beam theory. The present paper compares the inverse [K]−1 of the stiffness matrix derived from the assumed displacement function with the [F]exact. It is shown that the procedure also guarantees the implicit inclusion of rigid-body modes in the pertinent stiffness matrix [K]. Case studies on typical approximate displacement functions assure the appropriateness as well as the ease of application of the proposed method.
44 citations
TL;DR: The structural characteristics of the human knee have been determined using the stiffness influence coefficient method, where the nonlinear load-displacement data is approximated by a least squares polynomial and differentiated to determine the stiffness coefficient as a function of displacement.
43 citations
TL;DR: In modeling the fire response of reinforced concrete frame structures, the heat flow problem was separated from the structural analysis and two computer programs were written for solving the separate problems.
Abstract: In modeling the fire response of reinforced concrete frame structures, the heat flow problem was separated from the structural analysis and two computer programs were written for solving the separate problems. Both programs account for the temperature dependence of the thermal and mechanical properties of materials; the structural analysis accounts for the degradation of concrete and steel through cracking, crushing, spalling, and yielding. FIRES-T (FIre REsponse of Structures — Thermal) evaluates the thermal response of reinforced concrete elements using a nonlinear finite element approach coupled with time step integration. Using the thermal histories predicted by FIRES-T, FIRES-RC (FIre REsponse of Structures — Reinforced Concrete Frames) evaluates the structural response of reinforced concrete frames by a nonlinear, direct stiffness method coupled with time step integration. An iterative approach is used within time steps to find deformed shapes which result in equilibrium between forces associated with external load and internal stresses and degradation.
38 citations
TL;DR: In this article, the authors present a procedure for the automatic generation of symbolic stiffness matrices, which greatly reduces the amount of work involved in the construction of finite element stiffness matrix.
Abstract: Procedures for the automatic generation of symbolic stiffness matrices are presented that greatly reduce the amount of work involved in the construction of finite element stiffness matrices. The related system of programs is presented which completely automates the matrix generation and an example is given.
37 citations
TL;DR: Three main computing aspects encountered in the stress and strain analysis of the intact heart using the finite element technique, namely, the automatic partitioning of the myocardium of the heart into finite elements, the assemblage of the structural stiffness matrix of theMyocardium, and the storage and retrieval of its nonzero coefficients are described.
28 citations
TL;DR: In this article, a simple and direct procedure is presented for the formulation of an element stiffness matrix on element co-ordinates for a beam member and a beam-column member including shear deflections.
Abstract: A simple and direct procedure is presented for the formulation of an element stiffness matrix on element co-ordinates for a beam member and a beam-column member including shear deflections. The resulting stiffness matrices are compared with those obtained using the alternative formulation in terms of member flexibilities: The relative effects of axial force and shear force on the stiffness coefficients are presented. The critical buckling loads, considering the effects of shear force, are computed and compared with those available in the literature. Only prismatic members are considered.
21 citations
01 Jan 1977
TL;DR: In this article, a geometrical stiffness matrix suitable for the harmonic analysis of a shell of revolution is derived in a form which may accommodate high-order inter-element comparison functions.
Abstract: A geometrical stiffness matrix suitable for the harmonic analysis of a shell of revolution is derived in a form which may accommodate high-order inter-element comparison functions. Transverse shearing strains and nonlinear bending terms are included in the formulation. Condensation procedures which may significantly reduce the size of the resulting global matrices are described. The geometric stiffness matrix derived is incorporated into the formulation of two classes of problems, linear buckling and symmetrical incremental deformation, where the appropriate condensation techniques are developed.
8 citations
TL;DR: In this paper, the error in the computation of the elastic critical load of columns and rigid-jointed plane frameworks by the finite element method, as developed in general by Gallagher and Padlog and applied to frameworks by Hartz is determined.
Abstract: In this note the error in the computation of the elastic critical load of columns and rigid-jointed plane frameworks by the finite element method, as developed in general by Gallagher and Padlog and applied to frameworks by Hartz is determined. This error is computed on the basis of a comparison of the finite element method with the exact stability stiffness matrix method as described.
7 citations
TL;DR: In this paper, the energy expression associated with Poisson's equation is written, for triangular domains, in a form invariant to translation and rotation, and the element matrices derived from this depend only on the intrinsic parameters of the element, say the three sides.
Abstract: The energy expression associated with Poisson's equation is written, for triangular domains, in a form invariant to translation and rotation. The element matrices derived from this depend only on the intrinsic parameters of the element, say the three sides. Considerable savings in storage can be achieved by storing the global stiffness matrix in terms of these element matrices.
TL;DR: In this paper, an approximate stiffness method for the elastic analysis is described for rectangular orthotropic plates that are two-way continuous over rigid supports, where Levy-type displacement functions are used to derive stiffness matrices for full-size plate elements.
Abstract: An approximate stiffness method for the elastic analysis is described for rectangular orthotropic plates that are two-way continuous over rigid supports. Levy-type displacement functions are used to derive stiffness matrices for full-size plate elements. Transverse loads are replaced by nodal line forces. The number of degrees-of-freedom (stiffness equations) needed for acceptable approximations is very low.
TL;DR: In this article, critical load versus rise parameters for two different types of symmetric stiffness distribution and three cross-sectional area to moment of inertia relations were obtained through an approximate Ritz type approach for both types of instability, limit point and unstable bifurcation.
Abstract: Results in the form of critical load versus rise parameter are presented for two different types of symmetric stiffness distribution and three cross-sectional area to moment of inertia relations. Critical conditions are obtained through an approximate Ritz-type approach for both types of instability, limit point and unstable bifurcation. Exact solutions are obtained, whenever possible, which are used to provide a confidence factor for the approximate technique. Except for one special case, nonuniform stiffness geometries yield a stronger configuration than uniform stiffness geometries. In addition, for both nonuniform stiffness distributions considered, the more the stiffness is concentrated towards the center of the arch the stronger the arch.
TL;DR: In this paper, the static load-displacement behavior of circular foundations, embedded in an elastic stratum underlain by a rigid base, is investigated for various backfill conditions.
Abstract: The dynamic behavior of a structure resting on or embedded in an elastic material is a problem that has been of considerable interest in recent years. The determination of the dynamic soil-structure interaction effects is particularly important in the seismic design of nuclear power plants. The dynamic behavior of these structures has often been adequately described using a lumped parameter model consisting of equivalent mass, stiffness, and damping elements. For cases other then a foundation resting on the surface of an elastic homogeneous half space, numerical procedures, such as the finite element method, are frequently employed to determine these lumped parameters. To the extent that stiffness coefficients may be considered to be independent of frequency, the static had-displacement results of finite element models may be used to determine spring constants for the discrete model. This paper deals with the static load-displacement behavior of circular foundations, embedded in an elastic stratum underlain by a rigid base. Horizontal, rocking and coupled rocking-sliding stiffness are investigated for various backfill conditions.
TL;DR: In this article, the authors describe the derivation of the element stiffness factor for some familiar elements as needed in conjunction with the recently developed factor formulation of the stiffness for the matrix displacement method.