Showing papers on "Minimum weight published in 1978"

An advanced structural analysis/synthesis capability—ACCESS 2

Abstract: An advanced automated design procedure for minimum weight design of structures (ACCESS 2) is reported. Design variable linking, constraint deletion, and explicit constraint approximation are used to effectively combine finite element and nonlinear mathematical programming techniques. The approximation concepts approach to structural synthesis is extended to problems involving fiber composite structure, thermal effects and natural frequency constraints in addition to the usual static stress and displacement limitations. Sample results illustrating these new features are given.

An algorithm for optimal structural design with frequency constraints

Abstract: The paper presents a finite element method for minimum weight design of structures with lower-bound constraints on the natural frequencies, and upper and lower bounds on the design variables. The design algorithm is essentially an iterative solution of the Kuhn-Tucker optimality criterion. The three most important features of the algorithm are: (1) a small number of design iterations are needed to reach optimal or near-optimal design, (2) structural elements with a wide variety of size-stiffness may be used, the only significant restriction being the exclusion of curved beam and shell elements, and (3) the algorithm will work for multiple as well as single frequency constraints. The design procedure is illustrated with three simple problems.

Optimal design of dynamically loaded continuous structures

Abstract: A computational algorithm is developed and applied for optimization of beam and plate structures, subject to constraints on transient dynamic response. A continuous design formulation is retained, with dynamic response governed by partial differential operator equations. Adjoint equations are employed for sensitivity analysis and a function space gradient projection optimization approach is presented. Finite element analysis methods are applied for solution of the system dynamic and adjoint differential equations. Displacement constrained beam and plate minimum weight examples are solved, with a variety of boundary conditions.

Comparison of optimality criteria algorithms for minimum weight design of structures

Abstract: This paper presents a comparison of frequently used optimization algorithms based on optimality criteria to design a minimum weight structure. After summarizing the different methods, the relationship between the various algorithms is shown. They differ only in the degree of approximations made in formulating the recurrence relations to modify the design variables and to evaluate the Lagrange multipliers. A new iterative scheme, similar to Newton-Raphson, is also presented, with the equations written in such a form that it is not necessary to select the initial design vector of the unknown Lagrange multipliers. It is shown that with this scheme a minimum weight design can be obtained with a smaller number of analyses of the structure than with previously proposed methods.

ASOP-3: A Program for Optimum Structural Design to Satisfy Strength and Deflection Constraints

Abstract: Optimally criteria are applied in the iterative resizing of the elements of a finite-element model to achieve minimum weight. In addition to materials that can be considered to be homogeneous for analysis purposes, composite laminates with layups of considerable generality can be treated. Strength resizing of composite elements is done by treating the laminate as a unit, permitting the application of criteria consistent with current design practice. In addition, the program nominally treats a single generalized deflection constraint (linear combination of nodal deflections), but multiple constraints can be accommodated in many cases of practical interest by multiple submissions of the program. Results are presented for two representative lifting-surface structures, subject to both strength and twist constraints.

Minimum Weight Design of Cylindrical Shell with Multiple Stiffener Sizes

Abstract: The minimum weight design for the simply supported orthogonally stiffened cylindrical shell with smearedout and discrete stiffeners subjected to axial compression is studied by a method of multipliers. The method for constraint function minimization proposed by Fletcher and Powell and the quasi-Newton method are used and compared. The difficulty in the formidably expensive computations of eigenvalues in the optimization process is circumvented by an approximate buckling formulation using extremely simple displacement functions. Expensive exact eigensolutton is, however, performed for the optimized design variables to check the buckling load obtained by the approximate method. Seven design variables and fourteen inequality constraints are used for a design with a single stiffener size. Eleven design variables and twenty-one inequality constraints are used for a design with two stiffener sizes. The two designs are compared and discussed. From the calculations presented the design with two stiffener- sizes can be lighter than the one with one stiffener size.

Economic Design of Homogeneous I-Beams

Abstract: A procedure to find an economical design of homogeneous I-beams following the AISC (1973) specification has been presented considering the limitations imposed by the available plate thicknesses. Both stiffened and unstiffened beams are considered. A method is presented to find the flange plate cut-off points for the minimum weight design. Design charts are provided to readily find economical dimensions of an I-beam. Examples are given to illustrate the procedure.

Design method for optimum unstiffened girders

Abstract: The minimum weight design of constant height unstiffened plate girders has been formulated as a nonlinear optimization problem using the American Institute of Steel Construction specification The girders are assumed to be symmetrical and fully restrained against lateral buckling A two-stage minimization procedure is then employed to obtain minimum weight solutions The results of the study are in the form of simple design curves and formulas which can be used for any loading condition A rapid and accurate design method for plate girders with constant cross section is then proposed It is also shown how this design can be extended to allow for limitation on girder height, flange curtailment, and discrete values of plate thickness The study indicates that significant savings in material can be achieved when optimum girder proportions are employed instead of the widely used hot rolled steel sections

Minimum-weight design of multi-purpose tie-column of solid construction

Abstract: The paper provides the minimum-weight design of an elastic pin-ended member of solid construction under prescribed bounds on the maximum permissible elongation under axial tension and on the minimum allowable Euler buckling load. The member is to act as a tie for a part of its design life and as a column for the rest. Optimization for more than one design requirement not only unifies the design of mass-produced structural/mechanical elements, but also provides, at times, a practically acceptable design in that the optimal design does not have zero cross-sectional area at simply-supported ends—a situation quite common in optimal designs for a single requirement. However, it is shown that the constraints on longitudinal elongation and buckling load are less severe than that on the maximum stress. The effectiveness of optimization is judged by comparing the volume (mass) of the optimally designed member with that of a prismatic bar having the same buckling load.

Helical torsion springs for minimum weight by geometric programming

Abstract: Geometric programming is applied to solve a design optimization problem for minimum weight of torsional coil springs. An explicit solution of the optimization problem is obtained and applied to a numerical example.

Optimum design of bridge girders for electric overhead traveling cranes

Abstract: The problem of the design of box-type bridge girders for electric overhead traveling cranes is formulated as a minimum weight design problem with inequality constraints. The restrictions placed on the design problem include limitations on the maximum allowable deflections and stresses as well as on the shock absorbing capacity during accidental collision. The overall stability and rigidity considerations are also taken into account. Several load conditions, as per the code specifications, are considered in the design problem. The resulting nonlinear programming problem is solved by using an interior penalty function method. Numerical examples are given to illustrate the effectiveness of the approach. The resulting computer program is used to make a sensitivity analysis of the problem.

Optimum Design of Structures with Regard to Their Vibrational Characteristics : 5th Report, Minimum Weight Design with Many Constraints in Natural Frequencies

Abstract: In the first report, there has been presented a general method of structures in which natural frequencies are associated with objective functions or/and conditions of constraints. In the subsequent three report, the method has been demonstrated in two basic types of problems in this field, taking simple examples in vibration problems of rods, beams and beam-columns under various conditions. In this report, our study is devoted to more complicated optimum design problems in which minimum weight designs with many constraints on natural frequencies are of interest. For brevity, there both fundamental and the second natural frequencies are constrained. And it is shown that the proposed method in the first report is also applicable and effective to such kinds of complicated problems.

Maximum Load Design of Cold-Formed Steel-Channel Beams

Abstract: An alternative to minimizing the weight of a cross section for a specified load is to maximize the load capacity of a structural member of a specified weight. General conditions for equivalence of maximum load design and minimum weight design are given, and advantages of the former are pointed out. Application of the method to cold-formed channel beams results in general optimal relationships that can be expressed in very compact dimensionless form. It is concluded that in order to realize the maximum benefit of flange stiffening the web should also be stiffened. The optimal lip stiffener has a depth equal to the code minimum. Continuous spans are sometimes inferior to multiple single spans, and do not affect optimal profiles appreciably.

Minimum weight design of the statically indeterminate trusses

Abstract: In this paper, the optimization problem of minimum weight design of a statically indeterminate truss is formulated in explicit form. In case of a planar truss (if the geometry is fixed) there is a problem where the objective function is linear and the constraints are composed by a linear and a quadratic part or by a third degree and a fourth degree part, moreover the problem does not contain any equation.

Optimum Truss Geometry for Two Loading Conditions

Abstract: Variable node coordinates are considered for the case of minimum weight design under two alternative loading systems of simple ideal trusses. Optimality Kuhn-Tucker conditions are derived and used as the basis of two optimization methods. The first extends existing work on iterative design. The second uses a decomposition procedure combined with a gradient method.

Minimum Weight Design of Elastic Frame Structure by SUMT

Abstract: Some studies on optimization of structures are carried on by using of SMUT incorporated with matrix structural analysis. But this technique is difficult to achieve in practice because the cpu-time for calculation extremely increas as increasing of the structural members. Thus further works are needed to develop a satisfactory technique of optimizing the ship structures. In this paper following two techniques are investigated in order to improve SUMT.(a) Linearization of constraintsIt can be considered that the change of design variables at each iteration are generally small, then consider the Taylor series expansion of constraints about the starting point at the iteration up to linear terms. The constraints can be evaluated by the obtained linear formulas instead of by accurate analysis, number of structural analysis may be decreased.(b) Multi-step optimizationDivide whole structure into sub-structures, some design variables can be diminished by assuming that similar structural members which compose a sub-structure have equal dimensions. Optimizing the whole structure on the left design variables, the dimensions of the structural member obtained by such an optimization can be considered as approximation for actual optimum design. Repeat the same procedure using the approximate design as starting point and increasing the number of sub-structures.To compare the present methods to the normal one, several examples are performed by those methods. Application of linearization of constraints and multi-step optimization indicate that those techniques have good convergence property and computational efficiency, but it is shown that the multi-step technique is not effective for some cases.

Number of minimum-weight code words in a product code

Abstract: Consideration is given to the number of minimum-weight code words in a product code. The code is considered as a tensor product of linear codes over a finite field. Complete theorems and proofs are presented.

Optimum design of distributed mass and stiffness structural systems under constraints

Abstract: Shell structures are classic examples of distributed parameter systems. In this paper an approach is developed to obtain the optimum (minimum weight) configuration of a general shell structure subjected to simultaneous frequency and stress constraints. The constrained frequencies are determined by discretizing the shell using a finite-element technique and then minimizing special Rayleigh quotients defined for the finite-element model. The optimum configuration is determined by optimal decision of a vector of material and geometric design parameters using a modified Complex technique. The approach is demonstrated by application to a conical shell of elliptical cross-section subjected to inertial and externally applied loadings. An analytical solution to this problem, obtained using least squares techniques and Lagrange multipliers, is presented for comparison.

Filter weight minimization for rectified superconducting alternator power supplies

Abstract: Due to their very high power to weight ratio, rectified superconducting alternators are being considered as possible sources for a new generation of airborne dc power supplies Since these supplies are intended for very high power applications (tens of megawatts at several kilovolts), weight becomes a prime consideration in the design of the LC output filter Because of this problem, a considerable amount of research has been conducted to minimize the weight of the inductors and capacitors for these filters As a complement to this work, this paper describes a design algorithm that selects the minimum weight inductor and capacitor combination for a given set of specifications Since the behavior of the filter also depends upon the impedance offered by the machine, it is necessary to include the alternator model in the simulations