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.

Abstract: This paper studies the sensitivity analysis of the static structural compliance of symmetric layered composite plates with respect to the fiber orientation in terms of continuous and finite element discretized formulations. From the optimality criterion obtained based on the sensitivity analysis, it is found that the number of different angles of the fibers in an optimal plate is no more than 4 under rather general conditions. Making use of the sensitivity information and optimality criterion approach, we construct a mixed method for adjusting the fiber orientations to minimize the structural compliance of composite plates. Furthermore, the non-convcxity of compliances of composite plates is shown by numerical experiment.

Abstract: A dynamic programming formulation is proposed for finding all Pareto optimal solutions for a routing problem within a specified overall cost, overall time and overall distance A method is also proposed for finding other solutions which are not Pareto optimal solutions but which lie within the specified overall cost, overall time and overall distance

Abstract: The guide-weight criterion method is an efficient rational criterion method for the optimal design of antenna structures. The algorithm incorporates a set of recursion formulae derived from the Kuhn-Tucker conditions for a conditional extreme value. It has overcome the limitations of previous methods which had to neglect The change of load caused by change of design variables, and both member cross-sectional areas and coordinates of joints are included among the design variables in the new. Method. Compared with the virtual work approach developed by Levy, much better results are obtained in respect of both the rate of convergence and the final value of the objective function.

Abstract: The least weight design of cables under selfweight and uniformly distributed load is considered. The set of necessary conditions for an optimal solution is obtained using a new optimization approach based on a Lagrange multiplier and the gradient expression of the cost functional for a general class of optimal parameter selection problems, The proposed approach is shown to be simple and efficient in solving this class of optimization problems involving ordinary differential equations with algebraic constraints at end points. interestingly, the selfweight does not appreciably affect the length and profile of the optimal cable under uniformly distributed load as it would for other loading conditions. The cost sensitivity of the design is also investigated.

Abstract: This paper presents a new efficient mixed method for minimum weight structural design (geometrical and member sizing) of structures. The objective function is approximated by a second-order Taylor series expansion and the constraints by first-order Taylor series expansions. In order to eliminate the tedious work in evaluating the Hessian matrix and performing its inversion, an approximating matrix employed by the variable metric method is used to approach the inverse of the Hessian matrix. Applying the Kuhn-Tucker conditions to the problem, the K-T multipliers can be determinated by quadratic programming, and finally, the problem is transformed to one of linear programming with intercomplementarity conditions. The examples show that the method is generally applicable, convenient to use and has rapid convergence.

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.

Abstract: Charts are presented as the solution of the optimal shovel-truck configuration problem. In particular, for given parameters defining the shovel-truck operation (namely average haul, load and manoeuvre times), the charts enable the determination of the optimal truck fleet size. The objective function is one of cost per unit production of the operation. The model of the operation is based on finite source queueing theory results. Several queueing models are outlined and the sensitivity of the optimum solution to the assumed model is examined. Time and production constraints may be included with little extra work, The charts provide an effective and quick means for establishing the optimum truck fleet size in any earthmoving, quarrying or open-cut mining operation of the shovel-truck type.

Abstract: A shape and size optimization algorithm is developed to incorporate the shape and size variables in a recently developed machine tool simulation and design methodology known as Integrated Machining Process Design Simulator (IMPDS). This shape optimization algorithm, using coordinates of master nodes, parameters of geometric equations, coordinate linking and symmetry option approaches presents a general and flexible way of controlling and optimizing the structural shape of machine tool elements. An application of the proposed shape and size optimization algorithm indicates that the shape and size parameters have significant effects on the structural characteristics and the dynamic behavior of machine tool elements.

Abstract: The design of an Euler-Bernoulli beam is considered with two performance measures where the first one depends solely on the values of the state variables and the second one concerns only the minimization of the control effort required. The object is to generate the Pareto optimal solutions of the problem and determine an optimal trade-off between the performance measures while satisfying the stated constraints.

Abstract: The operating conditions are found for a batch chemical process that minimize the operating cost when given a weekly production rate. In solving for the optimum, a regression model is used along with a first principles dynamic model to reduce computation costs. Two nonlinear programming algorithms are used in sequence to both ensure reaching the true optimum and to reduce computation time. Computation costs were reduced ten fold. The value of local optima and a sensitivity analysis are also discussed.

Abstract: This paper presents an optimization principle for discrete-lime control problems that contains some elements of both the classical maximum principle and the optimality principle of dynamic programming. The applicability of this principle is shown by discussing three case studies: a warehousing problem, a production planning problem and the design of a pump-pipe system.

Abstract: This note points out that in the context of goal programming the linearization of nonlinear goals by logarithmic transformations, as it is usually done in the field of mechanical engineering applications, is not in general a valid method and can lead to wrong results.

Abstract: In this paper, an optimum design method is employed for a single ended flyback converter with four outputs. The mathematical model contains 16 variables and 16 constraints to minimize the weighted sum of the power loss and weight of the converter. The Augmented Lagrangian Multiplier Penalty Function Technique is adopted in forming the CAD program with FORTRAN IV. By treating the switching frequency as a constant in each computer run, a set of suboptimum design solutions were obtained by varying the frequency from 20 KHz to 60 KHz in 10 KHz steps. The U-shaped curve is observed by plotting the total loss characteristic against frequency. The following optimum design results are also obtained: 1) The optimum de duty ratio is about 0.3 to 0.34. 2) The converter should work at the critical mode between the discontinuous and current mode. 3) The air gap of the transformer core should be large enough (e.g.to 1.3 mm).

Abstract: Information theory is developed recently for application to communication engineering. This theory utilises the concept of “encoding” of messages such that the average length of a message is a minimum, and the efficiency of transmission of information is maximized. In an accurate synthesis of a function generating mechanism structural and mechanical errors should be considered together. Often, it is also required to control the error in a specified region of the range of function generation. An attempt is made to use the “encoding” procedure for the total error synthesis of a four-bar function generator such that the error in a specified region is kept under control.

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.

Abstract: The State-Space Gradient Projection Method is a versatile method for structural optimization. The convergence or otherwise of the: above algorithm is a function of many optimization parameters that are used in the algorithm. An attempt has been made to evolve suitable guidelines to the choice of these parameters for easy applicability to real life truss structures.

Abstract: Structural reanalysis technique methods are employed in structural optimization to analyze new designs efficiently using previous information. In this paper, an algorithm is developed to automatically select proper reanalysis techniques for efficient and accurate analysis during the machine tool structural element optimization process. This algorithm provides an error estimator to control the solution accuracy and a reanalysis capability to eliminate the problem dependency of using a single reanalysis technique. An example is used to demonstrate the advantage of this algorithm over the complete (exact) analysis or single reanalysis technique.

Abstract: A mixed integer approach for the least cost design of structural masonry walls with high eccentricities is developed. The integer variables in the approach are used to select the optimum values from a range of discrete block sizes, discrete grouting conditions, and discrete reinforcement levels. The structural constraints in the model are based upon the requirements of the Transformed Section type of analysis for masonry walls. The non-linear functions representing the relationships for determining the resisting capacities of the masonry element are approximated by linear functions which come very close in form and results to the original curves. Application of the model to an example problem demonstrates that in spite of the integer requirements, the approach is easily and efficiently solved using a standard software package.

Abstract: In many manufacturing situations materials are manufactured in rolls of standard (jumbo) lengths which have to be cut to various customer lengths so as to meet customer demands and also minimize waste. Such cases abound in paper, glass pipe, metal pipe, and other tubing industries, cellophane, and wood processing industries. The difficulty lies in figuring out which combination of the numerous possible cutting patterns to use to achieve the above-stated objective. This paper develops, for small- to mid-sized problems, a simple algorithm that generates all admissible cutting patterns for a given jumbo standard length and the customer demand (order) lengths. Such patterns will aid the decision making process or the cutting room engineer who may not have access to big mainframe computers for deciding the optimal pattern combination usually obtained by complex column generation schemes such as are found in the literature. A computer program written in BASIC language is coded and provided for easy and direct u...

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.

Abstract: This paper presents an application of generalized geometric programming to the optimal design of a prestressed concrete box bridge girder. The actual cost of construction consisting of prestressing. formwork and concrete is minimized. Constraints are formulated as stipulated by the British Code of Practice CP110. The constraints of the geometric program relate to bending and shear stresses, and geometric criteria. A sample design is presented and sensitivity studies are performed to test the influence of major design parameters on cost factors.