Showing papers on "Minimum weight published in 1986"
TL;DR: In this paper, an efficient and robust algorithm is developed for minimum weight design of space trusses with fixed geometry employing the general geometric programming (GGP) technique. But this algorithm is based on the virtual work method of structural analysis and the objective function is linear, subjected to linear size and stress constraints and nonlinear displacement constraints.
83 citations
TL;DR: In this paper, a non-convex variational problem with compliance constraints and plastic yielding constraints is considered, where the minimum weight is not achieved by any design, and the approximate designs oscillate as the element mesh is refined.
Abstract: A direct weight minimization subject to compliance constraints or plastic yielding constraints leads to a non-convex variational problem. Both the theoretical and the numerical analysis are unsatisfactory: the minimum weight is not achieved by any design, and the approximate designs oscillate as the element mesh is refined. We look for equivalent ‘relaxed problems’ with the same minima. They come from allowing composite materials constructed in an optimal way from the original materials. The constructions are different for elasticity and plasticity, but surprisingly the final relaxed problems are in some cases the same.
83 citations
TL;DR: In this paper, closed-form analytical solutions are presented for the analysis and design of minimum weight composite material hexcell and square cell honeycomb core sandwich and panels subjected to in-plane uniaxial compressive loads.
Abstract: Sandwich construction provides a very lightweight structural configuration for many load conditions The use of composite materials with their high stiffness, high strength, and anisotropy makes sandwich construction even more competitive for many applications It is very desirable to design these structures for minimum weight to insure their most effective use Closed-form analytical solutions are presented herein for the analysis and design of minimum weight, composite material hex-cell and square cell honeycomb core sandwich and panels subjected to in-plane uniaxial compressive loads These methods account for overstressing, overall buckling, core shear instability, face wrinkling, and monocell buckling The optimum face thickness, core depth, cell wall thickness, and cell size are analytically determined The methods insure minimum weight, as well as provide methods to compare various material systems, compare honeycomb sandwich construction with other panel architectures, and assess the weight penalties associated with using nonoptimum honeycomb sandwich constructions A comparison of various polymer, metal, and ceramic matrix composite materials is made by way of example
64 citations
TL;DR: An algorithm for the selection of a minimum weight truss, out of a set of possible candidate trusses, is presented and a technique, frequently used to keep second derivative approximations positive definite, is found to give numerical instabilities.
Abstract: An algorithm for the selection of a minimum weight truss, out of a set of possible candidate trusses, is presented. The trusses are subject to stress and deflection constraints. Multiple loading conditions are considered. Starling with a ground structure, a sequence of subtrusses called candidate trusses are generated and analyzed. Several criteria are used to rapidly discard non-optimal configurations. Sequential Quadratic Programming is used to solve a non-linearly constrained problem which is part of the algorithm. A technique, frequently used to keep second derivative approximations positive definite, is found to give numerical instabilities. Possible modifications to improve stability are discussed. Finally, three examples are given to demonstrate the algorithm.
44 citations
TL;DR: In this article, an analysis for the preliminary design of boxbeams made of fiber-reinforced composites is presented, which provides deflections, bending and torsional stiffnesses, stresses, and the conditions for buckling and first-ply failure.
Abstract: This paper presents an analysis for the preliminary design of boxbeams made of fiber-reinforced composites. The analysis provides deflections, bending and torsional stiffnesses, stresses, and the conditions for buckling and first-ply failure. Use of the analysis is illustrated through the example of a single cell, three bay, cantilevered box beam. This example demonstrates a design procedure for selecting the configuration which results in the required strength and stiffness at a minimum weight.
24 citations
TL;DR: In this paper, a method to efficiently solve the problem of minimum weight design of plane and space trusses with discrete or mixed variables is developed, which can also be applied to continuous variables.
Abstract: A method to efficiently solve the problem of minimum weight design of plane and space trusses with discrete or mixed variables is developed. The method can also be applied to continuous variables. The original formulation leads to a non-linear constrained minimization problem with inequality constraints, which is solved by means of a sequence of approximate problems using dual techniques. In the dual space, the objective function is to be maximized, depends on continuous variables, is concave and has first and second order discontinuities. In addition, the constraints deal simply with restricting the dual variables to be non-negative. To solve the problem an ad hoc algorithm from mathematical programming has been adapted.
Some examples have been developed to show the effectiveness of the method.
18 citations
TL;DR: In this article, the minimum weight of a honeycomb sandwich cylinder with the facings in composite material is obtained by an optimization method with the ply angles and the thicknesses of the ply and honeycomb as the design variables.
17 citations
TL;DR: In this paper, a general formulation of the minimum weight optimization problem is presented based on the concept of the expected value, and a solution of the corresponding mathematical programming problem has been obtained by means of indirect method.
15 citations
01 Jan 1986
TL;DR: In this article, the authors reviewed recent work on the optimal plastic design of plates, shells and shellgrids, and certain important conclusions are arrived at, such as the finding that the minimum weight design of solid plates and shells with a maximum thickness constraint contains a theoretically infinite number of rib-like formations.
Abstract: In this paper, recent work on the optimal plastic design of plates, shells and shellgrids is reviewed critically and certain important conclusions are arrived at. Of particular significance is the finding that the minimum weight design of solid plates and shells with a maximum thickness constraint contains a theoretically infinite number of rib-like formations. At relatively low load intensities, the layout of such ribs is furnished by the classical optimal grillage theory but at higher load levels a more advanced formulation is necessary. The latter has also been extended from optimal plastic design to optimal elastic design with stress, compliance and deflection constraints and this extended theory has been applied to plates. Moreover, it is shown that ribs in the solution can be suppressed by introducing additional geometrical constraints (termed “Niordson-constraints”) or segmentation.
13 citations
TL;DR: A modified simplex technique is described for the optimal plastic design of plane frames subject to one or more loading cases using a minimum weight criteria for the selection of relative member sizes.
12 citations
19 May 1986
TL;DR: The problem of minimum weight design with several natural frequency constraints is considered using a combined finite element-sequential linear programming (SCP) formulation and a simple adaptive move limit strategy is developed to stabilize the SLP solutions.
Abstract: The problem of minimum weight design with several natural frequency constraints is considered in this paper. The problem is solved using a combined finite element-sequential linear programming (SCP) formulation. The unique features of the current approach include the use of assumed mode reanalysis formulation for repeated eigensolution and the associated sensitivity analysis. Additionally, a simple adaptive move limit strategy is developed to stabilize the SLP solutions. The present approach has been implemented with general purpose finite element programs (MSC/NASTRAN and a version of SAP4) and applied to several design problems.
TL;DR: In this paper, a minimum-weight design of statically indeterminate beams subject to limits on normal and shear stresses is presented in a visual form using an existing CAD-package.
Abstract: The paper presents minimum-weight design of statically indeterminate beams subject to limits on normal and shear stresses. The loading consists of both external loads and self-weight. Analytical expressions for the stress constraints and the objective function are replaced by splines of desired order leading to a linear or non-linear programming problem (NLP) depending on the cross-sectional shape. It is found that the solution method based on a reduction of the NLP to a sequence of linear programs is the most efficient and reliable. The solution of the optimization problem is presented in a visual form using an existing CAD-package.
19 May 1986
TL;DR: In this paper, an efficient structural optimization methodology is presented for the design of minimum weight space frames subject to multiple natural frequency constraints, which is implemented in an automated structural optimization system which has been applied to solve a variety of space frame optimization problems.
Abstract: An efficient structural optimization methodology is presented for the design of minimum weight space frames subject to multiple natural frequency constraints. A powerful class of generalized hybrid c onstraint approximations which require o nly the first order constraint function d erivatives have been developed to overcome inherent nonlinearity of the frequency constraint. The generalized hybrid constraint functions are shown to be relatively conservative, separable and convex in the region bounded by the move limits based on the formula described in this paper. The optimization methodology is implemented in an automated structural optimization system which has been applied to solve a variety of space frame optimization problems. N umerical results obtained for three example problems indicate that the o ptimization methodology requires fewer than 10 complete normal modes analyses to generate a near optimum solution.
TL;DR: In this article, the minimum weight design problem for frame structures subject to stress and displacement constraints is treated and the cross-sectional dimensions are used as design variables and the hybrid approximation technique in combination with the dual method from mathematical programming is used.
TL;DR: In this paper, the minimum weight design of cylindrical water tanks is discussed. The design procedure used is a combination of the finite element analysis of structures and a numerical method of optimization.
Abstract: The paper deals with the minimum weight design of cylindrical water tanks. The design is to conform to BS5337. The design procedure used is a combination of the finite element analysis of structures and a numerical method of optimization. In the design, the internal radius and the height of the tank are fixed and the variation of wall thickness is treated as the unknown of the design. Only piecewise linear variations of thickness are considered. Results of some examples are presented and discussed.
TL;DR: In this paper, the minimum weight design of laminated fiber reinforced composite plate sub-fitted to inplane and transverse loading is attempted, where constraints on buckling load and transversal deflection are imposed.
Abstract: In this investigation, minimum weight d esign of laminated fiber reinforced composite plate sub- jected to inplane and transverse loading is attempted. Restrictions are imposed on buckling load and transverse deflection. Fiber orientation and thickness of each ply are t reated as design variables. Optimization studies a re carried out by using an unconstrained minimization technique. Numerical results have been obtained for anti- symmetric angle-ply l aminates treating number of plies as a parameter. Some of the observations are: (i) with preassigned fiber orientation, the optimum weight d esign results in a unique thickness distribution of plies; (ii) at low aspect ratios, stability constraint is active while deflection constraint is active at large aspect ratios.
TL;DR: In this article, the minimum weight design of orthotropic panels subjected to a supersonic flutter speed constraint and to a system of uniform in-plane loadings is studied.
Abstract: This paper deals with the minimum weight design of orthotropic panels subjected to a supersonic flutter speed constraint and to a system of uniform in-plane loadings. In approaching the problem, use is made of the methods of optimal control theory of distributed parameter systems. This leads to a set of necessary optimality conditions that, together with a supplementary condition ensuring that the flutter speed of the optimal panels coincides with the constrained one, constitute the governing optimality equations of the problem. An alternative form of the optimality equations is derived and a symmetry property of the optimal thickness distribution is placed in evidence. Numerical solutions are obtained via Galerkin's procedure, providing rough estimates of the optimal panel design. The results also show the influence of some important parameters, such as orthotropy ratio, in-plane loading, aspect ratio, and support conditions.
19 May 1986
TL;DR: In this article, the problem of minimizing the weight of a structure subject to coupled bending and torsional vibrations and frequency constraint has been studied, and the results have also been compared with those of the associated primal problem.
Abstract: The problem of minimizing the weight of a structure subject to coupled bending and torsional vibrations and frequency constraint has been studied in this paper. Stationary values of an appropriate objective function with both linear and nonlinear contraints have been discussed. Optimal designs of thin walled open section, with and without coupling effects have been compared. The results have also been compared with those of the associated primal problem.
TL;DR: In this article, two standard approaches to non-existence proofs are presented: the construction of suitable sequences and the use of necessary conditions, both within the context of contradiction proofs, illustrated with examples from optimal structural design ranging from the minimum weight design of an axially loaded rod to that of axisymmetrically loaded shells of revolution.
Abstract: Recently, much effort has been expended in establishing the well-posedness of optimal structural design problems. Experience indicates, however, that awareness of the non-existence of a solution may also be beneficial and can eliminate time wasted in searching for non-existing numerical or analytical optima. Two standard approaches to non-existence proofs are presented: the construction of suitable sequences and the use of necessary conditions — both within the context of contradiction proofs. The methods are illustrated with examples from optimal structural design ranging from the minimum weight design of an axially loaded rod to that of axisymmetrically loaded shells of revolution. It is shown that the causes of non-existence can be the choice of function space, boundary conditions, and a discontinuous dependence on parameters, among others. Some possible guidelines for a successful formulation of well-posedness in structural design are included.
22 Apr 1986
TL;DR: In this paper, an exponential number of greedy heuristics for minimum weight perfect matching of complete graphs of n vertices with edge weights satisfying the triangle inequality are presented. But the ratio of the weight of an approximate solution to that of an optimal solution is bounded by finite valued functions which depend only on n.
TL;DR: In this article, a general theory for elastic structures with prescribed deflections and constrained taper is proposed, which is applied to minimum weight beams with a linear relationship between the flexural stiffness and the cross-sectional area.
Abstract: This paper concerns a general theory for elastic structures with prescribed deflections and constrained ``taper'' (= rate of spatial change of the cross-sectional area). The proposed theory is applied to minimum weight beams with a linear relationship between the flexural stiffness and the cross-sectional area. This application is then illustrated through an example of a cantilever beam with constrained taper, having a prescribed slope at its free end. As this structure is statically determinate, the ``associated'' displacement field (that is, the Lagrangian for the equilibrium condition) is not employed directly in obtaining the soptimal solution. However, it can be used for checking the validity of the solution through a dual formulation. In this example, the optimal length of the section with constrained taper is given by another Lagrangian. In addition to verifying them through the dual formula, the results are checked by another independent method (differential calculus for an assumed class of soluti...
01 Jan 1986
TL;DR: In this article, the effect of passive damping on the optimum structural design with active control was investigated and the minimum weight design was obtained by imposing the constraints on the active damping parameter and the imaginary part of the closed-loop eigenvalues of the system for linear quadratic regulator.
Abstract: In this paper the authors have investigated the effect of passive damping on the optimum structural design with active controls. The minimum weight design is obtained by imposing the constraints on the active damping parameter and the imaginary part of the closed-loop eigenvalues of the closed-loop system for linear quadratic regulator. The integrated structural and control optimization problem is solved by using NEWSUMT-A program which is based on extended interior penalty function formulation. The ACOSS-FOUR model is selected for the study.
TL;DR: This work provides an efficient 2- quasi-greedy algorithm where a minimum weight base is constrained to have a fixed number of elements from two disjoint sets and gives theorems making it possible to jump over certain adjacent states, further increasing efficiency.
TL;DR: In this paper, the minimum weight design of cold-formed hat-shaped steel sections in accordance with the AISI (1968) specifications was carried out using a direct search method.
TL;DR: The design considered is the minimum weight design of columns with constant flange area but with varying web area, which is of uniform thickness and is tapered linearly.
Abstract: Optimum design of tapered steel I-columns is presented in the paper. The design considered is the minimum weight design of columns with constant flange area but with varying web area. The web is of uniform thickness and is tapered linearly. The column is assumed to be slender enough so as to permit an optimum proportioning based on elastic buckling. The problem is solved using an optimal parameter selection technique.
TL;DR: In this article, the minimum weight design of lattice portal frames is a nonlinear optimization problem which has been solved by using Rosen's gradient projection method, and the results of a parametric study carried out using the (OPTFRAM) computer program are presented for use in day to day design.
Abstract: Lattice portal frame structures fabricated using hot rolled angle sections for corner leg members laced together are often very economical systems for industrial structures. There is considerable flexibility in the design of such structures in terms of the spacings between and the unsupported lengths of corner leg members, besides the areas of the different elements of the frame. The minimum weight design of these frames is a nonlinear optimization problem which has been solved by using Rosen's gradient projection method. A computer program OPTFRAM, developed for the minimum weight design of lattice portal frames used in industrial structures, is described. This paper also presents the results of a parametric study carried out using the (OPTFRAM) computer program. Regression equations obtained from this study arc presented for use in day to day design.