Showing papers on "Minimum weight published in 1990"

Minimum-weight two-connected spanning networks

Abstract: We consider the problem of constructing a minimum-weight, two-connected network spanning all the points in a setV. We assume a symmetric, nonnegative distance functiond(·) defined onV × V which satisfies the triangle inequality. We obtain a structural characterization of optimal solutions. Specifically, there exists an optimal two-connected solution whose vertices all have degree 2 or 3, and such that the removal of any edge or pair of edges leaves a bridge in the resulting connected components. These are the strongest possible conditions on the structure of an optimal solution since we also show thatany two-connected graph satisfying these conditions is theunique optimal solution for a particular choice of ‘canonical’ distances satisfying the triangle inequality. We use these properties to show that the weight of an optimal traveling salesman cycle is at most 4/3 times the weight of an optimal two-connected solution; examples are provided which approach this bound arbitrarily closely. In addition, we obtain similar results for the variation of this problem where the network need only span a prespecified subset of the points.

Minimum weight design of rotorcraft blades with multiple frequency and stress constraints

Abstract: Minimum weight designs of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies are studied. Constraints are imposed on the minimum value of the blade autorotational inertia to ensure sufficient rotary inertia to autorotate in case of engine failure and on stresses to guard against structural failure due to blade centrifugal forces. Design variables include blade taper ratio, dimensions of the box beam located inside the airfoil and magnitudes of nonstructural weights. The program CAMRAD is used for the blade modal analysis; the program CONMIN is used for the optimization. A linear approximation involving Taylor series expansion is used to reduce the analysis effort. The procedure contains a sensitivity analysis consisting of analytical derivatives for objective function and constraints on autorotational inertia and stresses. Central finite difference derivatives are used for frequency constraints. Optimal designs are obtained for both rectangular and tapered blades. Using this method, it is possible to design a rotor blade with reduced weight, when compared to a baseline blade, while satisfying all the imposed design requirements.

Optimum design of space structures with active and passive damping

Abstract: This paper investigates the effects of passive damping on the optimum structural design with active controllers. An integrated design of structure and active control system is performed. The minimum weight design is obtained by imposing constraints on the closed-loop damping and the imaginary part of the closed-loop eigenvalues of the active control system. The mathematical optimization problem is solved by using the NEWSUMT-A program, which is based on quadratic extended interior penalty function method. The ACOSS-FOUR model is selected for the numerical studies. The active control effort, performance index, and optimum weights are presented as a function of the passive damping.

Influence of structural and aerodynamic modeling on optimization with flutter constraint

Abstract: The influences of structural and aerodynamic modeling on multidisciplinary optimization in an aeroelastic environment are not well understood. Therefore, optimizations with flutter and frequency constraints were performed to investigate the effects these modeling factors have on various representative wings. To this end, the Automated Structural Optimization System (ASTROS) was used as a tool to minimize the weight of various fully built-up finite element wing models in subsonic and supersonic flow under given flutter and frequency constraints. First, the performance of the optimization module was tested against results from other codes on a straight and uniform wing widely used for optimization with flutter constraints. Then, fully built-up finite element models of various wings with different aspect ratios were investigated for the influence on the structural optimization for minimum weight of the following modeling factors: finite element selection, structural grid refinement; number of selected modes, retention of breathing modes; selection of reduced frequencies to be used in flutter analysis; aerodynamic panel size and placement; splining of the aerodynamic grid to the structural grid selection of extra points of the structural wing box for splining; and number of constraints to be retained. Knowledge of these influences as well as of the program behavior is important, since optimization can be made more efficient by the selection of reasonable initial models. Also, it was shown previously that modeling has an impact on the results of modal and aeroelastic analyses. Thus, if modeling errors can negatively affect the analyses, a minimum weight optimization can be jeopardized and result in an optimal design that is rather unreliable. In the following, selected results are presented and the influences of some modeling parameters on optimization are pointed out.

Identities and approximations for the weight distribution of q-ary codes

Abstract: An explicit formula is derived that enumerates the complete weight distribution of an (n, k, d) linear code using a partially known weight distribution. An approximation formula for the weight distribution of q-ary linear (n, k, d) codes is also derived. It is shown that, for a given q-ary linear (n, k, d) code, the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q=q/sup -(n-k)/ as u becomes large. The error term is a decreasing function of the minimum weight of the dual. The results are also valid for nonlinear (n, M, d) codes with the minimum weight of the dual replaced by the dual distance. >

Study of Compression-Loaded and Impact-Damaged Structurally Efficient Graphite-Thermoplastic Trapezoidal-Corrugation Sandwich and Semisandwich Panel

Abstract: The structural efficiency of compression-loaded trapezoidal-corrugation sandwich and semisandwich composite panels is studied to determine their weight savings potential. Sandwich panels with two identical face sheets and a trapezoidal corrugated core between them and semisandwich panels with a corrugation attached to a single skin are considered. An optimization code is used to find the minimum weight designs for critical compressive load levels ranging from 3000 to 24thinspace 000 lb/in. Graphite-thermoplastic panels based on the optimal minimum weight designs were fabricated and tested. A finite-element analysis of several test specimens was also conducted. The results of the optimization study, the finite-element analysis, and the experiments are presented. The results of testing impact-damaged panels are also discussed.

Application of optimization methods to helicopter rotor blade design

Abstract: A procedure for the minimum weight design of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies, autorotational inertia, and centrifugal stress is presented. Optimum designs are obtained for blades with both rectangular and tapered planforms and are compared within a reference blade. The effects of higher-frequency constraints and stress constraints on the optimum blade designs are assessed. The results indicate that there is an increase in blade weight and a significant change in the design variable distributions with an increase in the number of frequency constraints. The inclusion of stress constraints has different effects on the wall thickness distributions of rectangular and tapered blades, but tends to increase the magnitude of the nonstructural segment weight distributions for both blade types.

Optimum design of thin-plated steel box columns

Abstract: This paper deals with the optimum design of thin-plated box columns subjected to axial thrust and biaxial end moments. Design formulae based on an effective width approach, proposed by the authors, are utilized in the optimization studies. The problem is first viewed as a strength maximization problem in which the optimum plate slenderness is evaluated for columns having constant weight of material. Results are presented in the form of nondimensional charts so that they can be used for practical design. The problem is then viewed as a minimum weight design problem and solved by means of the SUMT method. Side constraints, such as minimum plate thickness requirements, are imposed during the optimization process to study their effects on the design of box sections. Results are presented in terms of cross-sectional dimensions and minimum weights for columns having different proportions and subjected to different end loadings.

An improved fully stressed design algorithm for plate/shell structures

Abstract: The stress-ratio algorithm associated with fully stressed design philosophy has been used as a convenient tool to achieve minimum weight design of strength-limited structures. The algorithm is effective and converges quickly for many cases. However, it presents extremely slow oscillatory iteration histories for plate-thickness design problems that involve transverse bending loads. Modification of the basic algorithm presented in this paper provides an effective remedy to this problem when both membrane and bending loads are present. The modified resizing algorithm requires numerical solutions of a fourth-order algebraic equation. No additional data, beyond the ordinary static analysis results, are required.

On optimization of structural and control systems using a reduced order model

Abstract: An optimization method is presented to design a minimum weight structure with constraints imposed on the closed-loop frequency distribution and damping parameters. The control approach used here is linear quadratic regulator theory. The control model reduction is achieved by using Model Error Sensitivity Suppresssion. The application of the method is illustrated by designing the structure for different order of control models with the same constraints. The different designs obtained by these approaches are compared. The optimization problem is solved by using a nonlinear mathematical approach.

Quadratic residue codes of length 27

Abstract: The structure of the supports of minimum weight words for the quadratic residue codes of length 27 is determined. This does not depend on the alphabet field. From the global code one can create a ternary code with the same structure. >

On testing for improper error detection codes

Abstract: A family of tests for improper codes is given. These tests can be used in cases where the complete weight distribution of the code is unknown. It was found that knowledge of the number of minimum weight codewords can be used to greatly increase the effectiveness of the asymptotic Varshamov-Gilbert test. Further improvement is possible as more is known about the number of other weight codewords. >

Minimization on Stochastic Matroids

Abstract: : This work gives a methodology for analyzing matroids with random element weights, with emphasis placed on independent, exponentially distributed element weights. The minimum weight basic element in such a structure is shown to be an absorbing state in a Markov chain, while the distribution of weight of the minimum weight element is shown to be of phase-type. We then present two sided bounds for matroids with NBUE distributed weights, as well as for weights with bounded positive hazard rates. We illustrate our method using the transversal matroid to solve stochastic assignment problems.

ODE approach to minimum‐weight design of pinned columns in buckling

Abstract: The non-standard ordinary differential equations (ODEs), resulting from minimum-weight design of pinned columns in buckling, with or without the minimum cross-section constraints, are converted to an equivalent standard non-linear ODE system by using trivial ODE and interval mapping techniques. The ODE system is then directly and efficiently solved by the robust ODE code COLSYS. The longitudinal shapes and switching interface points sought are given explicily as part of the solutions with the accuracy satisfying the user pre-specified error tolerances. Compared with the analytical solutions, the numerical results obtained by this approach can be considered to be numerically exact.

Truss-core sandwich design via PANDA2

Abstract: The computer program PANDA2 for minimum weight design of composite, stiffened cylindrical or flat panels made of composite material is described. The capability of PANDA2 has been expanded to handle truss-core sandwich panels. The new capability is demonstrated in this paper with an example: minimum weight design of a truss-core sandwich panel under axial compression, in-plane shear, and normal pressure. At the design load the panel is in a locally postbuckled state.

Minimum weight design of laminated composites with strength constraints under a single in-plane loading.

Abstract: The present paper shows a reliable and efficient optimization approach on a minimum weight design of laminated composites under a single in-plane loading. Layer orientation angles as well as layer thicknesses are used as design variables, and the optimization technique is based upon a mathematical programming method. Transformed design variables with respect to the layer orientation angles in the principal loading direction are introduced to reduce the nonlinearity between strength constraints and design variables. A technique is also proposed to delete the strength constraints of almost zero thickness layers.

Optimization of the layout and cross section of plane frames with stress and buckling constrains.

Abstract: Optimization of the layout of plane frames as well as cross sections of the members under constraints of stress and global elastic buckling is presented based on the finite-element method and sequential linear programming. The critical load of in-plane global buckling is determined based on linear buckling analysis. Unlike the conventional shape optimization of cross sections, the nodal coordinates of the members as well as cross-sectional dimensions are constituents of design variables. When stress in a certain member is extremely low, or the length of a member or a cross-sectional dimension is extremely small, the member is removed according to given rules and thus the layout of the frame is automatically altered. Some examples of the minimum weight design of plane frames are presented. They show the availability of the proposed method.