Showing papers on "Minimum weight published in 1977"

Optimum design of laminated fibre composite plates

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.

Optimal layout of cantilever trusses

Abstract: For given allowable stress, Michell (Ref. 1) has investigated the optimal design of a cantilever truss that is to transmit a given load to two given fixed points of support. Disregarding the weight of the connections between the bars, he found that the truss of minimum weight is a truss-like continuum with an infinity of joints, and with bars that are mostly of infinitesimal length. In the present paper, a finite number of joints is enforced by including in the structural weight, which is to be minimized, not only the weight of the bars but also the weight of their connections, which is assumed to be proportional to the number of joints. The concept of two adjoint trusses is introduced, each of which coincides with the Maxwell diagram of the other truss. Two adjoint trusses have the same weight, and an optimal truss is therefore self-adjoint. The optimal configurations of 6-joint and 11-joint cantilever trusses are discussed, and the range of the weight of the typical joint is determined for which the 6-joint truss is optimal.

An Optimal Control Approach to Minimum-Weight Vibrating Beam Design

Abstract: A gradient projection algorithm is applied to a class of vibrating cantilever beam optimization problems which are formulated as optimal control problems The cross-section area is distributed along the beam for minimum total weight subject to fixed natural frequency constraints and a minimum allowed area limit Three topics receive major emphasis: the effects of shear deformation and rotary inertia, higher-mode frequency constraints, and multiple frequency constraints Computational results are presented for the cases of fixed fundamental frequency, fixed second-mode frequency, and fixed fundamental and second-mode frequencies under a variety of conditions

Discrete sizing of trusses for optimal geometry

Abstract: The optimal configuration and discrete member sizes are automatically determined to minimize the cost of three-dimensional indeterminate truss structures under multiple loading conditions. Member areas and joint coordinates are used as design variables. Design constraints include Euler buckling and specified limits on member stresses, member sizes, and joint displacements. Design variables may be linked and members can be deleted. The design process is separated into geometry modifications using the complex method and suboptimization using the stress ratio method and an analogous scaling procedure for displacement constraints. For each geometry change, discrete member sizes are selected from a table of allowable values. The method is applied to the cost minimization of a 25-member space truss using discrete steel angle sections that are chosen from a table satisfying AISC code requirements, and comparisons are made with minimum weight designs and with continuous variable methods.

Computer Program (OPTCOMP) for Optimization of Composite Structures for Minimum Weight Design.

Abstract: : The computer program OPTCOMP can be used to optimize or analyze a composite structure. The program uses an iterative procedure based on optimality criteria to design a minimum weight structure. The response of the structure to the applied loads is obtained by finite element analysis. The design variables are modified during each iteration by using a recurrence relation. The four strength criteria included in the program are maximum stress, maximum strain, Hill's criteria modified by Tsai and Norris criteria. The plate elements can be designed to prevent local buckling. The elements can be linked to have the same sizes if desired. A mixture of composite and metal structure can be designed by suitable definition of material properties. (Author)

Use of Galerkin's Method for Minimum-Weight Panels with Dynamic Constraints

Abstract: Galerkin's method is applied to the design of minimum-weight structures with dynamic constraints. The problems considered include the weight optimization of a simply supported beam and a panel, with the condition that their fundamental frequencies be the same as those of corresponding uniform-thickness structures. Galerkin's method also is used for the weight optimization of a semi-infinite panel and of a finite square panel, both of which have flutter speed constraints. Galerkin's technique is determined to be an effective method of finding approximate solutions to these structural optimization problems. The Galerkin solutions of the beam vibration and semi-infinite panel flutter problems compare favorably with exact numerical results. For the twodimensional problems of panel vibration and flutter panel, initial rough estimates of the minimum-weight thickness distribution are calculated.

Uniform shallow arches of minimum weight and minimum maximum deflection

Abstract: The present paper serves several purposes Besides presenting closed-form solutions to the problems in the title, it serves to illustrate the deduction of existence and nonexistence of solutions in this context, to point out some of the more or less known inadequacies of these design criteria and, finally, to provide the basis for a comparison with the natural structural shapes of shallow arches presented in another reference The minimum weight and minimum maximum deflection criteria both yield, as one possible optimal design, an arch on the verge of failure This is consequence of the fully-stressed design aspects of these criteria which, in this case, correspond to the maximum possible axial load However, meaningful results are obtained for a prescribed axial load in the minimum weight problem and for a given weight in the minimum of the maximum deflection problem

Minimum-Weight Design of Stiffened Cylinders Under Hydrostatic Pressure

Abstract: A methodology is developed by which one may design a stiffened cylinder of specified material, radius and length such that it can carry safely a given hydrostatic pressure which minimum weight. The solution is accomplished in two stages. First, design charts based on a simplified formulation of the objective function are obtained. Second, these design charts are used to evaluate the design variables. Such an approach enables the designer to introduce needed changes or avoid interaction of failure modes by paying the least weight penalty. Design examples are presented and the results are compared with those obtained by other investigators.

A multilevel approach for minimum weight structural design including local and system buckling constraints

Abstract: A rational multilevel approach for minimum weight structural design of truss and wing structures including local and system buckling constraints is presented. Overall proportioning of the structure is achieved at the system level subject to strength, displacement and system buckling constraints, while the detailed component designs are carried out separately at the component level satisfying local buckling constraints. Total structural weight is taken to be the objective function at the system level while employing the change in the equivalent system stiffness of the component as the component level objective function. Finite element analysis is used to predict static response while system buckling behavior is handled by incorporating a geometric stiffness matrix capability. Buckling load factors and the corresponding mode shapes are obtained by solving the eigenvalue problem associated with the assembled elastic stiffness and geometric stiffness matrices for the structural system. At the component level various local buckling failure modes are guarded against using semi-empirical formulas. Mathematical programming techniques are employed at both the system and component level.

Optimum design of composite box girder bridge structures.

Abstract: The practicality of optimization applied to a complex structural design problem is examined using the steel box girder bridge as a case for study. An automated procedure to generate and appraise cost differing layouts for a stiffened, open or closed steel box girder with composite concrete deck is described. Appraisal is based on the merrison interim design rules, CP 117 and BS 153. For comparison, the cost per metre of span is derived from a standard fabricated segment length of 10 M, using a breakdown of operation times with ascribed team plus plant rates and separate costing of material. A direct search technique with external penalty function is used to locate global optima. The procedure is applied to a numerical example in which minimum weight and minimum cost solutions are compared and the effects of changes in span and material grade are noted. It is concluded that the development of meaningful, special purpose, optimization routines for complex structures is possible and can be fruitful in technical and commercial terms provided the aim is to supplement rather than supplant engineering judgement. (A) /TRRL/

Minimum-weight codewords in the (128,64) BCH

Abstract: Techniques of combinational algebra and computer simulation are combined to determine the number of weight 22 codewords in the (128,64) BCH code which is being studied for use on future deep-space missions

Minimum-Weight Design of Stiffened Cylindrical Panels under Combined Loads

Abstract: Theme T HE increasing demand for lightweight structures has made the structural engineer more conscious of minimum-weight design. Since stiffened cylindrical shells have been used extensively during the past thirty years in underwater, surface, and aerospace vehicles, a tremendous effort has been exerted in designing such a configuration for minimum weight. A methodology was developed and demonstrated by the first author and his collaborators" for designing a stiffened cylinder, subjected to various load conditions with minimum weight when at least one of the active modes of failure is known a priori. The nonmenclature employed herein is identical to that of Refs. 1-4. Since the structural geometry of the above-mentioned vehicles (aircraft fuselage, submarine hull, etc.) is best represented by a combination of stiffened cylindrical panels, the methodology is, herein, applied to panels and extended to accommodate the combined application of loads. The precise statement of the problem considered, in this extension, is as follows: Given a stiffened thin cylindrical panel of specified material, radius of curvature, length and width, find the realistic size, shape, and spacing of the stiffeners, and the realistic thickness of the skin, such that the resulting configuration can safely carry a given set of surface loads with minimum weight.

An Optimality Criteria Approach to the Minimum Weight Design of Aircraft Structures.

Abstract: : The research presented in this report is both a continuation and an extension of the optimality criteria approach to structural optimization reported in AFOSR-TR-75-1431. In the present study the optimality criteria method is extended to provide a capability for the automated minimum weight design of elastic, redundant structures composed of one-and two-dimensional structural elements and subjected to multiple, independent static loading conditions. The design variables are taken to be the thicknesses of the structural elements. These variables are constrained to be between specified maximum and minimum values, as are the internal stresses in each element and the nodal displacements of the structure. Results are presented to indicate both the excellent performance of the optimality criteria method and the wide range of structures which can be designed using the algorithm. Finally, the algorithm is extended to include the new (to automated design) and very important requirement that structural integrity under the applied loads be maintained given the presence of existing structural fatigue cracks. This requirement, which is cast in an energy format and incorporated in the design algorithm as an inequality constraint, is shown to have a dominant effect in the design of safe, minimum weight aircraft structures. (Author)

Minimum Weight Design of Cylindrical Shell with Multiple Stiffener Sizes Under Buckling Constraint

Abstract: : The buckling equations for the orthogonally stiffened cylindrical shells under uniform axial compression and external pressure and with classical simply supported boundary conditions are formulated by treating the stiffeners as discrete elements. By assuming identical and equally spaced stringers and identical and equally spaced rings, the buckling equations can be uncoupled into several sets of simpler and manageable equations for the symmetric and antisymmetric longitudinal modes and symmetric and antisymmetric circumferential modes. The uncoupled submatrices are further reduced by partitioning and substitution. Effort is made to preserve the sparseness of the matrices in order to use a special compact storage scheme. A method to compute the minimum eigenvalue for a large general eigenvalue problem, the Ritz iteration method combined with Chebyshev procedure, is developed and its accuracies are evaluated. Examples are performed and results are compared to other computational and experimental results available.