Showing papers in "Mechanics of Structures and Machines in 1992"
TL;DR: Optimization of holonomic as well as non-holonomic multibody systems is presented as a nonlinear programming problem that can be solved with general-purpose optimization codes.
Abstract: Optimization of holonomic as well as non-holonomic multibody systems is presented as a nonlinear programming problem that can be solved with general-purpose optimization codes. The adjoint variable approach is used for calculating design derivatives of a rather general integral type performance measure with respect to design parameters. The resulting equations are solved by numerical integration backward in time. A multi-step integration algorithm with order and step-size control is adapted for this application by including an interpolation scheme. Numerical experiments and a comparison to the common approach of approximating the gradient of the performance measure by finite differences show that high efficiency, accuracy, and reliability are achievable.
117 citations
TL;DR: In this article, a shape design parameterization method that is built on the geometric modeler PATRAN is presented, where a number of geometric entities that represent structural design boundaries are parameterized, and a design parameter linking process can be performed to create geometric features from geometric entities.
Abstract: One of the major difficulties in structural shape optimal design is to create a design model by parameterizing a geometric model. Shape design parameterization is more complicated and difficult to handle than sizing design parameterization. First, the optimum shape is highly dependent on the design parameterization selected. An inappropriate design parameterization may result in an impractical design. On the other hand, changing the geometric shape of the design model to reflect successive changes in design parameters is a tedious, complicated, and inefficient process. Manual updates of geometric shape and finite element meshes are quite impractical. In this paper, a shape design parameterization method that is built on the geometric modeler PATRAN is presented. Using this method, a number of geometric entities that represent structural design boundaries are parameterized, and a design parameter linking process can be performed to create geometric features from geometric entities. To support the ...
72 citations
TL;DR: In this paper, the pb-2 Rayleigh-Ritz method was used for vibration analysis of elastic thin plates with arbitrary shape and boundary conditions, by using a Ritz function that consists of the product of a
Abstract: ABSTRACT This paper presents an efficient and accurate pb-2 Rayleigh-Ritz method for vibration analysis of elastic thin plates with arbitrary shape and boundary conditions. By using a Ritz function that consists of the product of a
39 citations
TL;DR: In this paper, a formulation for analysis of dextrous workspaces of manipulators is presented, including mobility-limited joints, full-range dexterity requirements, full range input requirements, and planar and spatial closed-loop kinematic structures.
Abstract: ABSTRACT A formulation for analysis of dextrous workspaces of manipulators is presented, including mobility-limited joints, full-range dexterity requirements, full-range input requirements, and planar and spatial closed-loop kinematic structures. A terminology for mechanism and manipulator models that permits specification of input, output, and dexterity requirements is proposed and demonstrated to yield broadly applicable conditions necessary for boundaries of dextrous workspaces. Row-rank deficiency of constraint sub-Jacobian matrices is shown to yield necessary conditions for boundaries of accessible output sets and dextrous accessible output sets that characterize the workspace and dextrous workspace, respectively, of both planar and spatial manipulators. Three closed-loop planar manipulators are analyzed in detail and a three-dimensional, closed-loop Stewart platform is formulated to illustrate applicability of necessary conditions
38 citations
TL;DR: In this paper, the effects of optimal shape design with orthotropic materials were investigated and an extensive study was performed, including design dependence on the analysis modeling, and combinations with thickness and ori-entational optimization were included.
Abstract: Orthotropic materials are now frequently used in engineering design. There is thus a need to understand the effects of optimal shape design with these materials. Stiffness as well as strength are direction-dependent, and designs that are rather different from optimal shapes should be expected with isotropic materials. This is confirmed in this paper. However, for minimum energy concentration and one load case, optimal designs still exhibit uniform energy density. For orthotropic materials, an extensive study is performed, including design dependence on the analysis modeling. In the last part of the paper, combinations with thickness and ori-entational optimization are included. It is concluded that established methods can be directly extended.
31 citations
TL;DR: In this paper, the dynamic instability of rectangular viscoelastic plates subjected to periodic in-plane loads P s + P d cos θt is investigated and the material behavior is given in terms of the Boltzmann superposition principle.
Abstract: The dynamic instability of rectangular viscoelastic plates subjected to periodic in-plane loads P s + P d cos θt is investigated. The material behavior is given in terms of the Boltzmann superposition principle, which allows any linear viscoelastic character. This representation yields an integro-differential equation of motion, for which time-dependent instability regions are determined analytically using the multiple-scales method. It is shown that, due to viscoelasticity, the stability regions are expanded relative to the elastic ones and that a plate which may be initially stable can become unstable after a finite time, unlike in the elastic case. The influence of the static and the dynamic parts of the loads on this region is also investigated.
12 citations
TL;DR: In this article, basic equtions of a model of beam in large strain and design sensitivity with respect to midline shape are presented. But they do not consider the effects of beam bending.
Abstract: Basic equtions of a model of beam in large strain and design sensitivity with respect to midline shape.
11 citations
TL;DR: In this paper, a two-step numerical analysis of a composite beam structure is presented, based on the idea of dividing the cross section into laminas, which leads to the estimation of the moment-curvature relation for different types of cross sections used in composite beams.
Abstract: ABSTRACT The two-step numerical analysis of a composite beam structure is presented in this paper. The first step, based on the idea of dividing the cross section into laminas, leads to the estimation of the moment-curvature relation for different types of cross sections used in composite beams. The second step adopts this constitutive relation, which is expressed in the space of generalized stresses and strains, into finite element nonlinear code. Some numerical examples are given, to show the agreement of numerical calculations with results of the authors' experiments, when the shrinkage of a concrete encasement and stresses due to welding processes in steel beams are considered. In addition, the numerical concept presented here seems to reduce the sensitivity of the final results obtained to finite element discretization error.
10 citations
TL;DR: In this article, the problem of indentation, with friction, of a rigid punch into an elastic half-plane is solved using Green's functions, and the problem is stated in terms of variational inequalities and discretized in both time and space.
Abstract: ABSTRACT The problem of indentation, with friction, of a rigid punch into an elastic half-plane is solved using Green's functions. The problem is stated in terms of variational inequalities and discretized in both time and space. The discrete variational inequaJities are then shown to be equivalent to an incremental problem, which after some additional reformulation can be solved as a linear complementarity problem. As is expected, friction effects make the problem load-path dependent, as shown by several numerical examples. The tangential stresses, in particular, show considerable load-path dependence.
10 citations
TL;DR: In this paper, it was shown that the internal forces in a truss are the ratios of two multilinear homogeneous polynomials in the longitudinal stiffnesses of the elements of the structure.
Abstract: Analytic expressions for member forces in linear elastic redundant trusses have recently been given by the author. It was shown that the internal forces in a truss are the ratios of two multilinear homogeneous polynomials in the longitudinal stiffnesses of the elements of the structure. The order of the polynomials is equal to the number of nodal degrees of freedom of the structure. The number of terms of each polynomial is equal to the number of statically determinate stable substructures that can be derived from the original structure. It was shown that coefficients of the polynomials can be computed through the equilibrium equations and by enforcing global compatibility of deformations. This paper generalizes these results to the case of linear elastic structures, composed of uniform prismatic elements that have extensional, flexural, and torsional stiffness. This is done by replacing each bi-modal bending element with a unimodal moment element and a unimodal shear element. This allows the rep...
9 citations
TL;DR: In this paper, a brief discussion on the geometrical imperfection sensitivity of elastic toroidal shells is provided, and the imperfections in meridian shape and thickness of the wall are taken into account and their influence on buckling pressure and postbuckling behavior is discussed.
Abstract: This paper is a supplement to one published in Mechanics of Structures and Machines in 1989 [1]. A brief discussion on the geometrical imperfection sensitivity of elastic toroidal shells is provided. The imperfections in meridian shape and thickness of the wall are taken into account and their influence on buckling pressure and post-buckling behavior is discussed. The results are compared for the shell of uniform thickness and the optimally distributed thickness of the wall [1].
TL;DR: In this paper, extended complex structures are represented as a furnished curve having a microstructure, and the presence of secondary structures is taken into account by adding a set of oscillators, allowing description of all types of vibration, e.g., longitudinal, torsional, bending, using the same approach.
Abstract: Extended complex structures are represented as a furnished curve having a microstructure. The presence of secondary structures is taken into account by adding a set of oscillators. This allows description of all types of vibration, e.g., longitudinal, torsional, bending, using the same approach. It is shown that the internal degrees of freedom of secondary structures act as a set of dynamic absorbers with respect to the carrier structure, thus providing considerable spatial absorption of vibration
Abstract: The subject of this work is the nonsmooth optimization of the midsur-face of a particular thin shell, the arch. Within the framework of the continuous model, nondifferentiable cost is chosen as the maximum of the square norm of displacements. In the theoretical portion of this paper, the existence of subgradients for this cost is demonstrated. It is then shown how the subgradients can be computed using an adequate adjoint state method. In the numerical portion of the paper, the implementation steps of the subgradient subroutine are detailed. Finally, results of numerical optimization for a case of uniform load and a case of non-uniform load are presented. With the aim of obtaining the shape with the best mechanical behavior, a comparison is made between non-differentiable cost optima and optima obtained for differentiable costs (such as the L2-norm of displacements). When the load is uniform, these optima are almost the same, but when the load is non-uniform, the optimum for the non-differentiabl...
TL;DR: In this article, second derivatives of an arbitrary functional with respect to these parameters are obtained, using the mixed approach in which both the direct and adjoint first-order solutions are used.
Abstract: For an arbitrary stress, strain, and displacement functional, second-order sensitivities with respect to varying structural shape are discussed. It is assumed that the external boundary of a structure can undergo shape modification described by a set of shape design parameters. Second derivatives of an arbitrary functional with respect to these parameters are obtained, using the mixed approach in which both the direct and adjoint first-order solutions are used. The general results are particularized for the case of the complementary energy of a structure.
TL;DR: In this article, the effects of initial geometrical imperfections are introduced by an "equivalent" fictitious load vector, acting on the ideal design structure, whose characteristics are evaluated so as to qualitatively reproduce the behavioral characteristics of a different structure affected by an unknown distribution of small geometry variations with respect to the design structure.
Abstract: A simple way of understanding initial geometrical imperfections in analytical models is presented. The effects of initial imperfections are introduced by an “equivalent” fictitious load vector, acting on the ideal design structure, whose characteristics are evaluated so as to qualitatively reproduce the behavioral characteristics of a different structure affected by an unknown distribution of small geometry variations with respect to the design structure. An approximate evaluation of the above-defined equivalent load is furnished and some numerical examples are presented to demonstrate the effectiveness of the method and suggest practical applications.
TL;DR: In this article, the mixed boundary problem is reduced to a pair of dual integral equations in the Hankel transform of the contact pressures, assuming that the layer is not exceedingly thin, and explicit forms for the layer's stiffness and the normal displacements of its surface.
Abstract: The lower surface of an elastic layer is fixed to a rigid base On the upper surface of the layer a cylindrical punch effects a normal displacement that is constant within a circular area The mixed boundary problem is reduced to a pair of dual integral equations in the Hankel transform of the contact pressures Assuming that the layer is not exceedingly thin, formal expressions for the stress components are determined, as well as explicit forms for the layer's stiffness and the normal displacements of its surface
TL;DR: In this article, the Reissner-type equations for the perfectly elastoplastic model of the shell are formulated on the basis of the geometrically nonlinear third-order theory.
Abstract: In the design of pipelines, a thermal expansion of the pipes is usually compensated for by a thin-walled, flexible shell of revolution, called a bellows. The process of cyclic loading of the structure may result in the formation of a sequence of plastic strain fields in the shell, which often leads to the collapse of the structure. Therefore, the question of whether the structure shakes down or collapses under the combined, cyclic loading is of particular importance to engineers The Reissner-type equations for the perfectly elastoplastic model of the shell are formulated on the basis of the geometrically nonlinear third-order theory. Various mechanisms of plastic collapse (e.g., maximal load or formation of plastic hinge) are discussed for the quasistatically loaded S-type bellows, as well as for the bellows subjected to cyclic, complex loadings. The analogy between these cases, as far as the failure modes are concerned, is explained. The adaptation (shakedown) and inadaptation (nonsymmetric alte...
TL;DR: In this article, an alternative method of formulating the equations of motion and using a computer-aided symbolic method for modeling of elastic mechanical systems is presented, derived from the principle of virtual work and cast in an expanded and closed form.
Abstract: In this paper an alternative method of formulating the equations of motion and using a computer-aided symbolic method for modeling of elastic mechanical systems is presented. The formalism is derived from the principle of virtual work and cast in an expanded and closed form. Symbolic generation of nonlinear closed-form equations of motion and their linearization are discussed. Symbolic equations for two examples are generated using the above method. Numerical results and comparison between full nonlinear and linearized robot models are presented
TL;DR: In this paper, a non-orthogonal series expansion of trigonometric functions for the elastic curve y of a beam or the deflection surface w of a plate is presented.
Abstract: ABSTRACT This paper presents a new solution method for several types of buckling and bending problems of beams and plates. The method is based on the use of a non-orthogonal series expansion, consisting of some specially chosen trigonometric functions for the elastic curve y of a beam or the deflection surface w of a plate. The calculations are performed using the Euler and Bernoulli polynomials, under realistic approximations of limiting values of the boundary conditions. In this method, it is not necessary to use the solution of the differential equation of the problem, Results obtained using the method are shown to be consistent with known solutions.
TL;DR: In this article, tools of nonsmooth optimization (subgradient method) are applied to perform design sensitivity analysis for some state-constrained distributed parameter control problems arising from sizing problems in structural design.
Abstract: Discretization of state-constrained optimal control problems and structural design problems often leads to optimization problems with non-dif-ferentiable objective functions. In this paper, tools of nonsmooth optimization (subgradient method) are applied to perform design sensitivity analysis for some state-constrained distributed parameter control problems arising from sizing problems in structural design. Moreover, design sensitivity analysis for optimal shape design problems with unilateral boundary value problems (Dirichlet-Signorini type problems) is considered.
TL;DR: In this article, a new explicitly solvable model of a unidirectional composite with nonlinear deformable fibers is introduced, which generalizes the shear-lag model by including the nonlinear behavior of fibers.
Abstract: A new explicitly solvable model of a unidirectional composite with nonlinear deformable fibers is introduced in this paper. This model generalizes the shear-lag model by including the nonlinear behavior of fibers. The equations of the model allow a Lax representation. This establishes the existence of an infinite number of invariants. The present theory is unique in that the analytical solution of the boundary value problem for simultaneous nonlinear differential equations is reduced to simultaneous nonlinear equations in terms of the boundary values of unknown functions. The two-dimensional multifilament failure problems of unidirectional fiber composites are analyzed. Example numerical solutions that focus specifically on the stress concentration factors of fibers adjacent to the local imperfections and the cracks are discussed.
TL;DR: In this paper, both minimum weight design (with eigenvalue constraint) and maximum eigen value (with total weight constraint) problems are addressed, based on the optimality conditions for an optimum design and the equation for the eigen problem.
Abstract: Methods of synthesizing discrete torsional vibration systems are developed in this paper. Both minimum weight design (with eigenvalue constraint) and maximum eigenvalue design (with total weight constraint) problems are addressed. Based on the optimality conditions for an optimum design and the equation for the eigenproblem, simple iterative design algorithms are derived. Two numerical examples are included to illustrate the proposed methods.
TL;DR: In this article, a material derivative method of shape design sensitivity analysis is extended to develop a continuum configuration design sensitivity method for built-up structures by accounting for effects of both shape and orientation changes in the same energy equation.
Abstract: Configuration design variation of built-up structures that include truss, beam, plane elastic solid, and plate design components can be characterized by changes in the domain shape and orientation of design components. The material derivative method of shape design sensitivity analysis is extended to develop a continuum configuration design sensitivity analysis method for built-up structures by accounting for effects of both shape and orientation changes in the same energy equation. Variations of energy bilinear and load linear forms, with respect to both shape and orientation design variables, are derived for each structural component. Using the adjoint variable or direct differentiation method, configuration design sensitivity results for built-up structures are obtained in terms of the design velocity fields. The relationship between design parameterizations and design velocity fields is discussed for line and surface design components. A numerical method is developed to evaluate these configu...