Showing papers on "Virtual work published in 1989"
TL;DR: In this paper, the geometric relations required for an embedded finite element representation of generally curved reinforcing bars or prestressing tendons are developed, and an inverse mapping procedure is developed to transform global coordinates of points on the reinforcement layer into local natural coordinates in the parent element.
Abstract: The geometric relations required for an embedded finite element representation of generally curved reinforcing bars or prestressing tendons are developed. For practical reasons, the reinforcing layers are described in global coordinates, independently of the finite element mesh. An inverse mapping procedure is developed to transform global coordinates of points on the reinforcement layer into local natural coordinates in the parent element. The strain field in the layer is discussed, including a bond slip model. The principle of virtual work is used to derive the various element matrices. The procedure is successfully tested, using both regular and irregular meshes, on three test problems: a uniform strain field, and two versions of a quarter ring under external pressure.
120 citations
TL;DR: In this article, the Euler Lagrange equilibrium equations and the associated static and Kinematic boundary conditions are compared with Vlasov, Chai Hang Yoo, and Papengelis and Trahair.
Abstract: The Thin-walled curved beam equatons are formulated using the principle of virtual work. The Euler Lagrange equilibrium equations and the associated static and Kinematic boundary conditions thus obtained are compared with Vlasov, Chai Hang Yoo, and Papengelis and Trahair. In and out of plane buckling of curved beam problems are solved and compared to published results.
104 citations
Book•
01 Jan 1989
TL;DR: In this article, a simple bar structure is analyzed with respect to a simple rigid-plastic theory and a simple linear elastic-perfectly plastic body is designed for a simple prismatic bar.
Abstract: 1. Basic Concepts and Notations. The mechanical properties of materials. Material models. Historical remarks. Notations. 2. Fundamental Relations and Governing Equations. Stress state. Strain state. Stress-strain relations. Constitutive equations of elastic-perfectly plastic bodies. The governing equations for linearly elastic-perfectly plastic bodies. 3. Variational Principles. Principle of virtual work and complementary virtual work. Variational principles of elasticity. Variational principles of plasticity. Discontinuity of stress and velocity fields. 4. Elasto-Plastic Analysis of Some Simple Problems. Analysis of a simple bar structure. Torsion of prismatic bars. Thick-walled spheres and cylinders under internal pressure. 5. Plastic Analysis of Plane Strain and Plane Stress Problems. Basic relationships. Plane plastic flow. Plane stress problems. Application of the finite element method. 6. Plastic Analysis and Design of Bar Structures. Yield condition for bar members. Elasto-plastic analysis. Limit analysis. Deflections. Plastic design. Application of mathematical programming. 7. Plastic Analysis and Design of Plates and Shells. Assumptions. Limit analysis of plates. Limit analysis of shells. Optimal design. 8. Various Inelastic Material Properties. Plastic hardening materials. Granular materials. Viscous materials. 9. Dynamic Plastic Response of Structures. Fundamental relationships. Simple rigid-plastic theory. Effect of strain rate sensitivity. Effect of large displacements. Effect of elastic deformations. Applications. Concluding remarks. References. Subject Index.
102 citations
TL;DR: A critical assessment of the 4-node assumed strain element as proposed by Dvorkin and Bathe is made in this paper, where the element performed excellently in all investigated shell problems which sometimes caused difficulties for other assumed strain techniques.
Abstract: A critical assessment of the 4‐node assumed strain element as proposed by Dvorkin and Bathe is made. The element performed excellently in all investigated shell problems which sometimes caused difficulties for other assumed strain techniques. For efficient computation in the non‐linear range, linearization of the virtual work equation is done to yield the consistent tangent stiffness. The shell formulation is done for stress and strain tensors based on local element coordinates. To demonstrate the effectiveness and rapid convergence of the non‐linear formulation, three examples are tested for large displacements.
86 citations
TL;DR: In this article, the authors describe a continuum principle of design sensitivity analysis of linear and nonlinear structures for shape and nonshape optimization problems, which is more convenient to interpret and discretize for numerical calculations.
69 citations
TL;DR: In this article, a continuum-based, laminated, stiffened shell element is used to investigate the static, geometrically nonlinear response of composite shells, where the element is developed from a three-dimensional continuum element based on the incremental, total Lagrangian formulation.
Abstract: A continuum-based, laminated, stiffened shell element is used to investigate the static, geometrically nonlinear response of composite shells. The element is developed from a three-dimensional continuum element based on the incremental, total Lagrangian formulation. The Newton-Raphson method or modified Riks method is used to trace the nonlinear equilibrium path. A number of sample problems of unstiffened and stiffened shells are presented to show the accuracy of the present element and to investigate the nonlinear response of laminated composite plates and shells. INITE-ELEMENT analyses of the large displacement the- ories are based on the principle of virtual work or the associated principle of stationary potential energy. Horrigmoe and Bergan1 presented classical variational principles for non- linear problems by considering incremental deformations of a continuum. A survey of various principles in incremental form in different reference configurations, such as the total Lagran- gian and updated Lagrangian formulations, is presented by Wiinderlich.2 In the total Lagrangian description, all static and kinematic variables are referred to the initial configura- tion. Finite-element models based on such formulations have been used in the analysis of arch and shell instability prob- lems.3'6 A special numerical technique must be adopted to trace the path of the load-deflection curve near the limit point (i.e., critical buckling load) and in the postbuckling region, because the stiffness matrix in the vicinity of the limit point is nearly singular, and the descending branch of the load-deflec- tion curve in the postbuckling region is characterized by a negative-definite stiffness matrix. Many methods have been proposed to solve limit-point problems. Among these are the simple methods of suppressing equilibrium iterations,7'8 the introduction of artificial spring,3 the displacement control method,7'8 and the "constant-arc-length method" of Riks. 11-12 Reviews of these most commonly used techniques are con- tained in Refs. 13 and 14. Among these methods, the modified Riks method appears to be the most effective in conjunction with the finite-element method. Many investigators11'15 have used this method in its original or modified form to determine the pre- and postbuckling behavior of various types of struc- tures such as arches, shells, and domes. In most of these works, only isotropic material was considered. Very few works of the nonlinear buckling analysis of laminated com- posite structures are reported in the literature.16 When solving the problems of shells with stiffeners by the finite-element method, a beam element whose displacement pattern is compatible with that of the shell is required. In analyzing eccentrically stiffened cylindrical shell, Kohnke and Schnobrich17 proposed a 16-deg-of-free dom (DOF) isotropic beam finite element that has displacements compatible with
31 citations
Book•
01 Jan 1989
TL;DR: In this article, the stiffness method for three-dimensional structures has been described, using the basic equations and using virtual work to compute the stiffness of the structural components, such as beams and planar frames.
Abstract: Symbols and notation. Introduction. The stiffness method using the basic equations. The stiffness method using virtual work. The stiffness method for beams and planar frames. The stiffness method for three-dimensional structures. Special topics for the stiffness method. The flexibility method. Appendices. Index.
24 citations
TL;DR: In this article, a virtual work principle of virtual work is proposed for thermo-elastic bodies from it are derived the equations of motion, the Cauchy stress principle and the Gibbs relations.
Abstract: A principle of virtual work is proposed for thermo-elastic bodies From it are derived the equations of motion, the Cauchy stress principle and the Gibbs relations The principle is also used to analyse the response of internally constrained bodies
16 citations
TL;DR: In this paper, the viscous boundary for a full three dimensional interaction system was derived by virtual work, and the effectiveness of the boundary was examined in detail, and it was found that the proposed boundary showed good energy absorption, in contrast with previous formulation.
Abstract: Since a region analyzed by the FEM must be finite, artificial boundaries are introduced into the model when a widely extending area such as infinite ground is analyzed. Special boundary conditions have been proposed for the artificial boundaries, such as a viscous boundary.Although the commonly used viscous boundary has less ability to absorb energy, the boundary has many merits, for example, such as the applicability for nonlinear problem and simplicity of coding for computer programs. These merits are very important, especially for three dimensional nonlinear problems.In this study, the viscous boundary for a full three dimensional interaction system was derived by virtual work. The effectiveness of the boundary was examined in detail, and it was found that the proposed viscous boundary showed good energy absorption, in contrast with previous formulation.
14 citations
TL;DR: In this article, the authors derived the equations of motion for vehicles with directionally sliding wheels by means of the virtual work method and determined the required driving torques from them by using the pseudo-inverse matrix.
12 citations
TL;DR: In this article, a rational procedure for determining the "kick-off forces" of a four-node quadrilateral plate element is presented. But the procedure used in NASTRAN violates a virtual work condition and leads to difficulties in certain warped configurations.
TL;DR: In this paper, the Lagrange's dynamic equations are presented in a fashion suitable for introductory robotics courses, and the thrust of the demonstration is that, given dynamic for a rigid body, one can always manipulate the equations to show that the equations depend exclusively on the difference between the total kinetic and potential energies of the system.
Abstract: The topic of Lagrange's dynamic equations is presented in a fashion suitable for introductory robotics courses. The development of the material does not rely on either principles of virtual work or variational calculus. The thrust of the demonstration is that, given dynamic for a rigid body, one can always manipulate the equations to show that the equations depend exclusively on the difference between the total kinetic and potential energies of the system. >
TL;DR: In this paper, a complete reciprocal formulation of the conjugate structure method is presented by means of a correspondence between two systems, each consisting of a space curved bar resting on an external medium.
Abstract: By means of a correspondence between two systems, each consisting of a space curved bar resting on an external medium, a complete reciprocal formulation of the conjugate structure method is herein presented. The method allows us to transform (internal and external) forces and deformations of one of the two systems into deformations and forces respectively of the conjugate one. This can be done by interchanging the field equilibrium and the mechanical boundary conditions in the two systems with the field compatibility equations and the kinematical boundary conditions and vice versa. The reciprocal correspondence descends from the Principle of Virtual Work and it can be regarded as a particular form of this principle. The Culmann and Ricci ellipse theories and the Cross column analogy are shown as particular aspects of the unified method. The equilibrium, compatibility equations and constitutive laws of the one‐dimensional space member supported on an external medium are derived in a suitable form. An appli...
TL;DR: This work is working on the design of a general animation system, including generation of motion defined by use of mechanical laws, in an audiovisual environment and uses a dynamical formalism based upon the principle of virtual work associated with LAGRANGE's multipliers that takes into account holonomic and nonholonomic constraints.
Abstract: We present an analysis of unified animation control processes. The design of an animation system is strongly coupled with the considered application. Most of the existing systems are specialized. For example, in audiovisual production or in C.A.D., only a few systems specialized in mechanical computation have capabilities in the image synthesis field. We are working on the design of a general animation system, including generation of motion defined by use of mechanical laws, in an audiovisual environment. Our system is built around a structured graph in which we store a hierarchical description of the objects and mechanical joints. The joints may be used to link the objects together to allow the building of multibody mechanical systems. For objects which are not submited to mechanical laws, motion control can be specified by key-framing techniques or explicit trajectories. We use a dynamical formalism based upon the principle of virtual work associated with LAGRANGE's multipliers and that takes into account holonomic and nonholonomic constraints. The generation of the differential motion equations system is automatically built by performing symbolic derivations. These equations are then solved for each time step and give object locations and orientations.
TL;DR: In this article, the authors considered a collapse load analysis of a prestressed concrete slab with unbonded tendons and derived the virtual work of forces exerted by the tendons on the remaining part of the structure, treated as a free body.
TL;DR: In this article, a virtual force method for solving shakedown limit λ √ N √ I √ d N is introduced. But the authors consider the elastic deformations of a structure as the virtual displacements of the residual moment in the structure so that the virtual work equations of the relative moment can be expressed and solved by a mathematical programming method.
Abstract: In this paper, a virtual force method for solving shakedown limit λ\N\I\ds\N is introduced. The elastic deformations of a structure are taken as the virtual displacements of the residual moment in the structure so that the virtual work equations of the residual moment can be expressed and solved by a mathematical programming method. It is mentioned that comprehensive combinations of failure mechanisms are not necessary for the solution and thus it is most suitable for computational analysis.
01 Jan 1989
TL;DR: In this article, a hierarchical sequence of finite element models for beams, arches, plates and shells based on the principle of virtual work is described, and the exact solutions corresponding to models in the hierarchic sequence converge to the exact solution of the fully three-dimensional problem of linear elasticity.
Abstract: Formulation of hierarchic sequences of finite element models for beams, arches, plates and shells based on the principle of virtual work is described. The exact solutions corresponding to models in the hierarchic sequence converge to the exact solution of the fully three-dimensional problem of linear elasticity. The stopping criterion is that the functionals of interest must be substantially independent of the choice of the model. This process is closely related to p-extensions. Aspects of implementation are discussed in connection with axisymmetric shells and an example is presented. An application of superconvergent extraction methods for the computation of stress resultants is demonstrated.
TL;DR: Necessary and sufficient conditions for the finiteness of moments of virtual work for GI/GIc queues are presented in this paper, where the authors consider the case of single-server queuing.
Abstract: Necessary and sufficient conditions for the finiteness of moments of virtual work for GI/GIc queues are presented. REGENERATIVE; ACTUAL WORK; REMAINING SERVICE TIME; FAST SINGLE-SERVER QUEUE
TL;DR: In this article, a method for solving the nonlinear dynamic problem of moderately thick plates and shells is presented using an incremental finite element method. Butts et al. developed an incremental force-displacement relationship using the principle of virtual work.
01 Jan 1989
TL;DR: In this paper, a technique to determine the force and torque relationship between the joints and end effector of a general manipulator with flexible links is presented, which accounts for the link's bending and torsion.
Abstract: A technique to determine the force and torque relationship between the joints and end effector of a general manipulator with flexible links is presented. A systematic technique which accounts for the link's bending and torsion is used to determine the kinematic equations of the manipulator. The Jacobian matrix is modified to account for the links' flexibility. Using the principle of virtual work, a force and torque relationship between the joints and end effector is obtained which accounts for the links' flexibility. Results obtained experimentally are compared to computer simulations of the resulting force and torque relationships to demonstrate the validity of the theories. >
TL;DR: In this article, it is shown that under certain admissibility conditions, forcing the satisfaction of the constitutive equations, yields the energy and the so-called pure complementary energy functionals as subsets.
Abstract: The classical linear stability equations for columns take the form of equilibrium equations in terms of displacements. From a variational point of view these equations emerge as conditions of extremum from an energy or virtual work functionals. In principle it should be possible to arrive at the governing equations for stability of columns from a complementary energy or complementary virtual work functional involving force quantities alone. This is rarely done. Both the energy and the complementary energy approaches depend upon the relevant constitutive equations. In this study a formulation is employed wherein focus is maintained on the constitutive equations. It is shown that under certain admissibility conditions a least squares functional, forcing the satisfaction of the constitutive equations, yields the energy and the so-called pure complementary energy functionals as subsets.
01 Jan 1989
TL;DR: In this paper, the authors present a discretisation of the finite element method based on variational principles (or virtual work principles), which can also be derived from weighted residual procedures.
Abstract: As mentioned in Chap. 2, in most cases, closed form analytical solutions to all but the simplest type of continuum problems are very difficult or even impossible to obtain. Therefore, the discretisation of continuum problems is necessary to obtain numerical solutions for practical purposes. There have been several general techniques directly applicable to the differential equations governing the problems. Such methods include finite difference approximations, various weighted residual procedures, or approximate techniques of determining the stationarity of properly defined “functionals”. However, for the last two decades, the most powerful discretisation tool has been widely acknowledged to be the finite element method which is based on variational principles (or virtual work principles). The method can also be derived from weighted residual procedures.
TL;DR: In this article, the effects due to an arbitrary location of the load point on the buckling and post-buckling behavior of elastic thin-walled beams are investigated, based on the virtual work equation of linearized finite displacement.
Abstract: The effects due to an arbitrary location of the load point on the buckling and post-buckling behaviour of elastic thin-walled beams are investigated. The governing differential equations and the corresponding stiffness matrices are derived, based on the virtual work equation of linearized finite displacement. Numerical examples are given to investigate the behaviour of I, channel and zee shaped beams. Location of load point greatly affects the post-buckling behaviour as well as the buckling loads. Although zee and channel sections show a large reserve strength as compared with I-section, this reserve strength corresponds to fairly large stresses and displacements.
TL;DR: A derivation for the finite element equations of consolidation by the principle of virtual work and virtual complementary work provides a simple alternative to derivation by variational principles or the Laplace transform.
Abstract: A derivation for the finite element equations of consolidation by the principle of virtual work and virtual complementary work is presented. This provides a simple alternative to derivation by variational principles or the Laplace transform. In the final part of the paper the equations are rearranged into a form suitable for time stepping for non‐linear applications.
01 Jan 1989
TL;DR: In this article, a tectnique to determine the force and torque relationship between the manipulator's joints and end effector for a general manipulator with flexible links is presented.
Abstract: In the paper. a tectnique to determine the force and torque relationship bet- the manipulator's joints and end effector for a general manipulator with flexible links is presented. First a systematic technique which accounts for the links' bending and torsion is used to determine the kinematic equations of the manipulator. Next the Jacobian matrix is malified to accwnt for the links' flexibility. Using the principle of virtual work, a force and torque relationship bet- the joints and end effector is obtained which accounts for the links' flexibility. Results obtained experimentally are compared to computer simulations of the resulting force and torque relationships to demonstrate the validity of the theories developed.
TL;DR: In this paper, a theoretical method for calculating the deflections due to bending and shear is developed, using the virtual work principle for beams, for Japanese cedar, the simplified bi-linear σ-e relationship with a linear falling branch, according to compression and tension tests.
Abstract: Materials such as timber, concrete, rock and soil exhibit a strain softening behavior after reaching a peak stress in compression tests. The present paper is concerned with deflections of elastic-plastic strain softening timber beams. The theoretical method for calculating the deflections due to bending and shear is developed, using the virtual work principle for beams. For Japanese cedar, the simplified bi-linear σ-e relationship with a linear falling branch is used, according to compression and tension tests. The shearing stresses of timber beams in the elastic-plastic range are also presented. The numerical solutions obtained from the presented virtual work principle are compared with the test results, and the accuracy and the efficiency of this method may be verified.
01 Jan 1989
TL;DR: In this article, the fundamental notions of fracture mechanics (the mechanics of cracked bodies) in the framework of analytical mechanics are described and conditions of equilibrium and stability are stated in terms of generalized forces.
Abstract: The aim of this paper is to describe the fundamental notions of fracture mechanics (the mechanics of cracked bodies) in the framework of analytical mechanics. The principle of virtual work for systems with unilateral constraints is used. A classification is proposed for states of the system “cracked body — loading” with respect to equilibrium and stability properties. Conditions of equilibrium and stability are stated in terms of generalized forces. The relationship between generalized forces and conventional concepts of fracture mechanics (energy release rate, stress intensity factors, path-independent integrals) is discussed. The fatigue crack growth is also presented in terms of analytical mechanics under the additional assumption that the resistant generalized forces depend on the level of microdamage accumulated near the crack-tips.
01 May 1989
TL;DR: A brief survey is given of some recent developments in finite-element analysis technology which bear upon the three main research areas under consideration in this workshop: (1) analysis methods; (2) software testing and quality assurance; and (3) parallel processing.
Abstract: A brief survey is given of some recent developments in finite-element analysis technology which bear upon the three main research areas under consideration in this workshop: (1) analysis methods; (2) software testing and quality assurance; and (3) parallel processing. The variational principle incorporated in a finite-element computer program, together with a particular set of input data, determines the exact solution corresponding to that input data. Most finite-element analysis computer programs are based on the principle of virtual work. In the following, researchers consider only programs based on the principle of virtual work and denote the exact displacement vector field corresponding to some specific set of input data by vector u(EX). The exact solution vector u(EX) is independent of the design of the mesh or the choice of elements. Except for very simple problems, or specially constructed test problems, vector u(EX) is not known. Researchers perform a finite-element analysis (or any other numerical analysis) because they wish to make conclusions concerning the response of a physical system to certain imposed conditions, as if vector u(EX) were known.