Showing papers in "International Journal for Numerical Methods in Engineering in 1977"
TL;DR: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems and boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits as mentioned in this paper.
Abstract: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems—structural mechanics being only one of these. Boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits. In this survey of the field we show how such procedures can be utilized in conventional FEM context.
711 citations
TL;DR: In this paper, a simple and efficient finite element is introduced for plate bending applications, where Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration, and the element is surprisingly accurate.
Abstract: A simple and efficient finite element is introduced for plate bending applications. Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is surprisingly accurate.
647 citations
577 citations
TL;DR: Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid-side node near the crack tip at the quarter point, are shown to embody the (1/√r) singularity of elastic fracture mechanics and the ( 1/r)-singularity of perfect plasticity as discussed by the authors.
Abstract: Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid-side node near the crack tip at the quarter point, are shown to embody the (1/√r) singularity of elastic fracture mechanics and the (1/r) singularity of perfect plasticity. The procedure of performing the fracture analysis for the case of small scale yielding is discussed, and the finite element results are compared with theoretical results.
The proposed elements have wide application in the fracture analysis of structures where ductile fracture is investigated. They permit a determination of the relationship between crack tip field parameters, loading, and geometry. And for a given fracture criterion can be applied to the prediction of fracture in structures such as pressure vessels under in service conditions.
563 citations
TL;DR: In this article, the wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined, and appropriate boundary conditions are described, for finite and infinite boundaries.
Abstract: The wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined. Appropriate boundary conditions are described, for finite and infinite boundaries. These equations are then presented in a variational form, which is used as a basis for finite and infinite elements. The elements are used to solve a wide range of unbounded surface wave problems. Comparisons are given with other methods. It is concluded that infinite elements are a competitive method for the solution of such problems.
428 citations
TL;DR: In this paper, the features of an advanced numerical solution capability for boundary value problems of linear, homogeneous, isotropic, steady-state thermoelasticity theory are outlined.
Abstract: The features of an advanced numerical solution capability for boundary value problems of linear, homogeneous, isotropic, steady-state thermoelasticity theory are outlined. The influence on the stress field of thermal gradient, or comparable mechanical body force, is shown to depend on surface integrals only. Hence discretization for numerical purposes is confined to body surfaces. Several problems are solved, and verification of numerical procedures is obtained by comparison with accepted results from the literature.
341 citations
TL;DR: This report presents a package of efficient, reliable, well-documented, and portable FORTRAN subroutines for solving NxN system of linear equations M x = b, where the coefficient matrix M is large, sparse, and nonsymmetric.
Abstract: : Consider the NxN system of linear equations M x = b, where the coefficient matrix M is large, sparse, and nonsymmetric. Assume that M can be factored in the form M = L D U, where L is a lower triangular matrix, D is a diagonal matrix, and U is a unit upper triangular matrix. Such systems arise frequently in scientific computation, e.g., in finite difference and finite element approximations to non-self-adjoint elliptic boundary value problems. This report presents a package of efficient, reliable, well-documented, and portable FORTRAN subroutines for solving these systems.
296 citations
TL;DR: In this paper, two efficient numerical methods for dealing with the stability of linear periodic systems are presented, which combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period.
Abstract: Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.
269 citations
TL;DR: In this paper, a formulation for the transient analysis of space frames in large displacement, small strain problems is presented, where node orientations are described by unit vectors and deformable elements are treated by a co-rotational (rigid-convected) description.
Abstract: A formulation is presented for the transient analysis of space frames in large displacement, small strain problems. For purposes of treating arbitrarily large rotations, node orientations are described by unit vectors and deformable elements are treated by a co-rotational (rigid-convected) description. Deformable elements may be connected either to nodes directly or through rigid bodies. The equations of motion are integrated by an explicit procedure. Sample results are presented on the snap-through of an arch-type structure and an idealization of a vehicle-barrier impact.
198 citations
150 citations
TL;DR: In this article, a simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation using a transmission-line modelling (TLM) method is described, and a detailed comparison of the new TLM methods and the well established methods is made.
Abstract: This paper describes a simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation using a transmission-line modelling (TLM) method. The paper also shows that the explicit finite difference routine and the implicit Crank–Nicolson routine may be expressed as the exact solution of certain transmission-line models. Using these models a technique for comparing the accuracy and stability of numerical routines is developed and a detailed comparison of the new TLM methods and the well established methods is made.
TL;DR: In this paper, an interative approach is proposed for the numerical analysis of elastic-plastic continua, which gives after convergence an implicit scheme of integration of the evolution problem, and is concerned with elastic-perfectly plastic materials and with hardening standard materials.
Abstract: An interative approach is proposed for the numerical analysis of elastic–plastic continua. This approach gives after convergence an implicit scheme of integration of the evolution problem, and is concerned with elastic-perfectly plastic materials and with hardening standard materials. Under a generalized assumption of positive hardening, the proof of convergence of the iterative solutions is given. Some numerical examples by the finite element method are also discussed.
TL;DR: In this article, a method for the minimum weight optimum design of laminated fiber composite plates, subject to multiple inplane loading conditions, which includes stiffness, strength and elastic stability constraints, is presented.
Abstract: A method is presented for the minimum weight optimum design of laminated fibre composite plates, subject to multiple inplane loading conditions, which includes stiffness, strength and elastic stability constraints. The buckling analysis is based on an equivalent orthotropic plate approach leading to two uncoupled eigenproblems per load condition. Overall computational efficiency is achieved by using constraint deletion techniques in conjunction with Taylor series approximations for the constraints retained. The optimization algorithm used, namely the method of inscribed hyperspheres, is a sequence of linear programs technique which exhibits rapid convergence in this application. Several example problems are given to demonstrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.
TL;DR: In this paper, a finite element formulation is described for problems with solution functions known to have local rλ variation (s), 0<λ<1, and thus singular gradients. But the conditions of continuity, low order solution capability, and accurate numerical integration of the singularity element are discussed with a view towards establishing the general range of applicability.
Abstract: A finite element formulation is described for problems with solution functions known to have local rλ variation (s), 0<λ<1, and thus singular gradients. Special 3-node triangular elements encircle the singularity and focus to share a common node at the singular point. The shape function of each triangle has the appropriate r λ mode and a smooth angular mode expressed in element natural co-ordinates. As with standard elements, the unknowns are the nodal values of the function. Even if the precise angular form of the asymptotic solution is known, the formulation makes no attempt to embed it, but instead piecewise approximates it. This allows assembly of the element coefficient matrix using standard procedures without nodeless variables and bandwidth complications.
The conditions of continuity, low order solution capability, and accurate numerical integration of the singularity element are discussed with a view towards establishing the general range of applicability of the formulation. Numerical applications to the elastic fracture mechanics problems of composite bondline cracking and crack branching are discussed.
TL;DR: In this paper, a general formulation of the incremental equations of motion for structures undergoing large displacement finite strain deformation is presented, based on the Lagrangian frame of reference, in which constitutive models of a variety of types may be introduced.
Abstract: The paper presents the theoretical and computational procedures which have been applied in the design of a general purpose computer code for static and dynamic response analysis of non-linear structures A general formulation of the incremental equations of motion for structures undergoing large displacement finite strain deformation is first presented These equations are based on the Lagrangian frame of reference, in which constitutive models of a variety of types may be introduced The incremental equations are linearized for computational purposes, and the linearized equations are discretized using isoparametric finite element formulation Computational techniques, including step-by-step and iterative procedures, for the solution of non-linear equations are discussed, and an acceleration scheme for improving convergence in constant stiffness iteration is reviewed The equations of motion are integrated using Newmark's generalized operator, and an algorithm with optional iteration is described A solution strategy defined in terms of a number of solution parameters is implemented in the computer program so that several solution schemes can be obtained by assigning appropriate values to the parameters The results of analysis of a few non-linear structures are briefly discussed
TL;DR: In this article, a two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells.
Abstract: A two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point of numerical integration is essential for its success when applied to thin shells where the results compare favourably with those achieved with more complex curved elements.
TL;DR: In this paper, an algorithm for optimal design of elastic structures, subjected to dynamic loads, is presented, which minimizes structural weight subject to constraints on displacement, stress, structural frequency, and member size.
Abstract: This paper presents an algorithm for optimal design of elastic structures, subjected to dynamic loads. Finite element, modal analysis and a generalized steepest descent method are employed in developing a computational algorithm. Structural weight is minimized subject to constraints on displacement, stress, structural frequency, and member size. Optimum results for several example problems are presented and compared with those available in the literature.
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.
TL;DR: In this paper, a self-correcting approach based on load and displacement incrementation is presented for pre-and post-buckling analysis of finite element systems. But, the postbuckling problem has been less actively pursued probably because of the inherent numerical difficulties encountered.
Abstract: The prediction of nonlinear structural behavior by the finite element method wherein buckling does not occur has received considerable attention and, with it, reasonable success has been achieved. However, the post-buckling problem has been less actively pursued probably because of the inherent numerical difficulties encountered. This note reviews very briefly the numerical methods currently being used for pre- and post-buckling analysis and presents a self-correcting approach based on load and displacement incrementation which is shown to be efficient, reliable, and easy to program. Numerical solutions are presented which demonstrate the effectiveness of the method.
TL;DR: In this paper, an integral equation method is presented for the numerical calculation of the eigenvalues of the scalar Helmholtz equation, using a particular solution instead of Green's function, the calculations could be simplified due to the elimination of complex numbers.
Abstract: An integral equation method is presented for the numerical calculation of the eigenvalues of the scalar Helmholtz equation. By using a particular solution instead of Green's function, the calculations could be simplified due to the elimination of complex numbers.
TL;DR: In this article, a strategy for solving problems involving simultaneously occurring large deflections, elastic-plastic material behaviour, and primary creep is described, which involves a double iteration loop at each load level or time.
Abstract: SUMMARY A strategy for solving problems involving simultaneously occurring large deflections, elastic-plastic material behaviour, and primary creep is described. The incremental procedure involves a double iteration loop at each load level or time. In the inner loop the material properties are held constant and the non-linear equilibrium equations are solved by the Newton-Raphson method. These equations are formulated in terms of the tangent stiffness. In the outer loop the plastic and creep strains are determined and the tangent stiffness properties are updated with use of a subincremental algorithm. The magnitude of each time subincrement is determined such that the change in effective stress is less than a preset percentage of the effective stress. The strategy is implemented in a computer pogram, BOSOR 5, for the analysis of shells of revolution. Examples are given of elastic-plastic deformations of a centrally loaded flat plate and elastic-plastic-creep deformations of a beam in bending. The major benefits of the subincremental technique are the increased reliability with which problems involving non-linear plastic and timedependent material behaviour can be solved and the greatly relaxed requirement on the number of load or time increments needed for satisfactory results.
TL;DR: In this paper, the elastohydrodynamic lubrication problem is solved by using a finite element procedure and the Newton method, and the numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling.
Abstract: The elastohydrodynamic lubrication problem, in which the lubricant pressure and film thickness are sensitive to surface deformation, is solved by using a finite element procedure and the Newton method. The numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling. The present analysis shows that pressure spikes are formed near the outlet region, a result which has been found in the line contact problem and which has been conjectured in the present problem.
TL;DR: In this article, the effects of anisotropy and shear deformation on the accuracy and convergence of shear-flexible displacement finite element models are considered, and numerical results show the effect of increasing the order of approximating polynomials and of using derivatives of generalized displacements as nodal parameters.
Abstract: Two aspects of the finite element analysis of mid-plane symmetrically laminated anisotropic plates are considered in this paper. The first pertains to exploiting the symmetries exhibited by anisotropic plates in their analysis. The second aspect pertains to the effects of anisotropy and shear deformation on the accuracy and convergence of shear-flexible displacement finite element models. Numerical results are presented which show the effects of increasing the order of approximating polynomials and of using derivatives of generalized displacements as nodal parameters.
TL;DR: In this article, a finite element method is used to calculate the stress intensity factors for three-dimensional geometries containing a number of depths of crack subjected to various loads, with results accurate to within 1 per cent or 4 per cent (depending on case) of known solutions.
Abstract: Finite element methods are used to calculate the stress intensity factors for three-dimensional geometries containing a number of depths of crack subjected to various loads. Special elements are used at the tip to represent the variation of the displacement with respect to the square root of the distance from the tip. The stress intensity factors are determined by comparison of the displacements in the special elements, by a method of virtual crack extensions, and, in one case, by an integral around the tip. With meshes containing between 50 and 100 quadratic isoparametric elements, results accurate to within 1 per cent or 4 per cent (depending on case) of known solutions are demonstrated.