Nonlinear buckling optimization of composite structures

The paper presents an approach to nonlinear buckling fiber angle optimization of laminated composite shell structures. The approach accounts for the geometrically nonlinear behaviour of the structure by utilizing response analysis up until the critical point. Sensitivity information is obtained efficiently by an estimated critical load factor at a precritical state. In the optimization formulation, which is formulated as a mathematical programming problem and solved using gradient-based techniques, a number of the lowest buckling factors are included such that the risk of “mode switching” during optimization is avoided. The presented optimization formulation is compared to the traditional linear buckling formulation and two numerical examples, including a large laminated composite wind turbine main spar, to clearly illustrate the pitfalls of the traditional formulation and the advantage and potential of the presented approach.     

Optimization formulations for the maximum nonlinear buckling load of composite structures

This paper focuses on criterion functions for gradient based optimization of the buckling load of laminated composite structures considering different types of buckling behaviour. A local criterion is developed, and is, together with a range of local and global criterion functions from literature, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization.     

A multilevel genetic algorithm for optimization of geometrically nonlinear stiffened composite structures

A multilevel genetic algorithm aiming the global optimization of beam reinforced composite structures with nonlinear geometric behaviour is proposed. A unified approach based on load-displacement control for buckling and first ply failure analysis is adopted. The Newton-Raphson iterative scheme and the arc-length method are used for tracing the equilibrium path and later for updating the critical values. The proposed genetic algorithm performs several sequences of two optimization levels resulting from the decomposition of the original optimization problem. Independent genetic searches are implemented for each level where different fitness functions and sub-populations are considered. The genetic operators selection and crossover supported by an elitist strategy are used while the diversity of the sub-populations is guaranteed based on implicit mutation. A genetic material exchange between levels is performed using clones and so the offspring of matured sub-populations is guaranteed. To improve the efficiency of the multilevel genetic optimization a niche of population is induced after the first stage at both levels.     

Design sensitivity analysis and optimization for nonlinear buckling of finite-dimensional elastic conservative structures

The purpose of this review paper is to summarize the existing methods of design sensitivity analysis and optimization of elastic conservative finite-dimensional systems with respect to nonlinear buckling behavior. Difficulties related to geometrical nonlinear singular behaviors are discussed in detail. Characteristics of optimized structures are demonstrated in reference to snapthrough behavior, hill-top branching, and degenerate critical points. A new optimization result of a flexible truss that fully utilizes the snapthrough behavior is also presented.     

Shape optimization of buckling sensitive structures

The optimal design of structures with distinct geometrically non-linear behavior has attracted a great deal of interest in the last years mainly with respect to sizing for prescribed external loads. In the present contribution a method is proposed to maximize the critical load under certain constraints, e.g. for a given volume, allowing varying shape as well as cross-sections. The combination of direct computation of the critical load and path-following methods is integrated into a general optimization procedure consisting of mathematical programming techniques, sensitivity analysis and computer aided geometric design methods. The formulation includes imperfection sensitivity as an important part within the optimization process.     

A unified approach to optimization of structural members under general constraints

A unified numerical approach, based on a control parameterization technique, for solving structural crosssectional optimization problems is presented. The key factor to the unified formulation lies in the framing of the objective functional and the constraints into the same unified canonical form. Consequently, the different types of objective functionals, geometrical and performance constraints can be treated in the same way, thus paving the path for the problems to be solved under a single approach using a general purpose software. To demonstrate this versatile approach, several illustrative examples of cross-sectional shape optimization of structural members under a variety of constraints were examined.     

A random set approach to the optimization of uncertain structures

The single-objective optimization of structures, whose parameters are assigned as fuzzy numbers or fuzzy relations, is presented in this paper as a particular case of the random set theory and evidence theory approach to uncertainty. Some basic concepts concerning these theories are reviewed and the relationships among interval analysis, convex modeling, possibility theory and probability theory are pointed out. In this context a frequentistic view of fuzzy sets makes sense and it is possible to calculate bounds on the probability that the solution satisfies the constraints. Some special but useful cases illustrate in detail the meaning of the approach proposed and its links with a recent formulation conceived within the context of convex modeling. Some theorems allow a very efficient computational procedure to be set up in many real design situations. Two numerical examples illustrate the model presented.     

A unified aggregation and relaxation approach for stress-constrained topology optimization

In this paper, we propose a unified aggregation and relaxation approach for topology optimization with stress constraints. Following this approach, we first reformulate the original optimization problem with a design-dependent set of constraints into an equivalent optimization problem with a fixed design-independent set of constraints. The next step is to perform constraint aggregation over the reformulated local constraints using a lower bound aggregation function. We demonstrate that this approach concurrently aggregates the constraints and relaxes the feasible domain, thereby making singular optima accessible. The main advantage is that no separate constraint relaxation techniques are necessary, which reduces the parameter dependence of the problem. Furthermore, there is a clear relationship between the original feasible domain and the perturbed feasible domain via this aggregation parameter.     

A level set topology optimization method for the buckling of shell structures

Structural and Multidisciplinary Optimization - Shell structures are some of the most widely used in engineering applications. Flat plates, stiffened panels, and wing ribs are each examples of...     

A unified approach to smoothing formulas

Based on various approaches, several different solutions to the smoothing problem have been given. The relationships between these solutions are not immediate, although they solve the same problem. Making use of a certain framework from scattering theory, we derive two families of solutions, with equations evolving forwards and backwards in time, respectively. Within these families three major previous approaches are obtained as special cases, and their relationships are clarified. The set of solutions also contains as a fourth special case a (new) backwards analog of the innovations solution. The Mayne-Fraser two-filter formula belongs to the set of backwards solutions, and within this framework certain difficulties with its interpretation can be resolved.     

A unified approach to layout wirability

We consider the problem of wiring planar knock-knee mode layouts. We present a systematic approach to this problem and develop a unified framework that also applies to layouts using grids that are more general than the usual square grid, and determine all possible grids that satisfy some natural regularity criteria. We develop some specific techniques for wiring of layouts in the square grid. As one of the applications of these techniques, we give a simple characterization of two-layer wirability of an arbitrary layout.On leave from the Institute of Computer Science, Polish Academy of Sciences, P.O. Box 22, 00-901 Warsaw, Poland. W. Lipski tragically died on May 30, 1985.The work of F. P. Preparata was supported in part by the Semiconductor Research Corporation under Contract SRC RSCH 84-06-049.     

A unified approach to pattern recognition

The paper is an outline of a new approach to pattern recognition developed by the author. A fuller introduction to the approach will appear soon.⁽¹⁾ Within the proposed framework the two principal approaches to pattern recognition—vector and syntactic—are unified.     

Robot reachability problem: A nonlinear optimization approach

The reachability of a robot manipulator to a target is defined as its ability to move its joints and links in free space in order for its hand to reach the given target. This paper presents a way of testing the reachability of a robot to given target. The target could be a three dimensional object represented by a cuboid, a line or merely a point.The reachability test problem is transformed into a nonlinear optimization problem, which is solved by using the Tunneling Algorithm [1–3].The paradigm of the Tunneling Algorithm is described in detail. Several examples of testing the reachability of two robots to given targets are presented and the results are compared with that of the existing RGRG algorithm [5]. The results of comparisons show that the Tunneling Algorithm is better than the RGRG algorithm. It can always obtain the correct answers of testing, and it is effective and suitable to solve the reachability test problem.This project is partially supported by a grant from Martin Marietta (ORNL) 19x-55902V. Also this project is partially funded by ONR grant N00014-94-1-0343.     

Multilevel optimization of laminated composite structures

A two-stage optimization method aiming at the optimal design of shells and plates made of laminated composites has been developed. It is based on a mixture of sensitivity analysis, optimality criteria and mathematical programming techniques. The design variables are the optimality criteria and mathematical programming techniques. The design variables are the macro-element thicknesses and the layers' angles. Weight minimization with material efficiency maximization are the objectives with constraints on stresses and displacements. Maximization of the material efficiency is performed at one level using the conjugated method applied to the angles of the macro-element layers keeping the thicknesses constant. The other level is dedicated to weight reduction using optimality criteria and using as variables the macro-element thicknesses with the angles of the macro-element layers constant.     

A unified approach for stability analysis of a class oftime-varying nonlinear systems

It is shown that an integral with negative feedback from its output terminal through a strictly passive system is still strictly passive. By using successive negative feedback around integrals, the conditions of strict passivity and a unified approach for constructing strictly passive systems are obtained for time-varying nonlinear systems of different orders. A new concept of “dissipation factor” is defined in this paper. The stability of a class of time-varying nonlinear systems is examined by using this passivity analysis     

An optimization approach to nonlinear diagnostic filter synthesis

We consider the synthesis problem for diagnostic filters based on nonlinear models of the systems being diagnosed. To solve the problem, we propose a new approach that unites the methods of algebra of functions and differential geometry when performing a nonlinear transformation of the original mathematical model for the diagnosed system with linear optimization techniques. An advantage of the proposed approach is that it overcomes principled obstacles of existing diagnostic filter synthesis methods and gets a solution for systems with parametric uncertainties.     

A primal-dual backtracking optimization method for blended composite structures

A combinatorial optimization method is proposed for finding the optimal stacking sequence and the ply drop-offs of a blended composite structure. This method assumes that the thicknesses of the regions of the structure are fixed in advance. It is able to handle efficiently design and manufacturing rules which are of combinatorial type. The optimization problem is formulated as a constrained binary programming problem and it is solved by applying both a primal and a dual backtracking procedures with a local search method. Some numerical experiments are carried out to show the efficiency of the optimization method with respect to both computational time and quality criteria.     

A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators

In this paper, for joint torque optimization of redundant manipulators subject to physical constraints, we show that velocity-level and acceleration-level redundancy-resolution schemes both can be formulated as a quadratic programming (QP) problem subject to equality and inequality/bound constraints. To solve this QP problem online, a primal-dual dynamical system solver is further presented based on linear variational inequalities. Compared to previous researches, the presented QP-solver has simple piecewise-linear dynamics, does not entail real-time matrix inversion, and could also provide joint-acceleration information for manipulator torque control in the velocity-level redundancy-resolution schemes. The proposed QP-based dynamical system approach is simulated based on the PUMA560 robot arm with efficiency and effectiveness demonstrated.     

A unified approach to structural weight minimization

It is shown that the two classical approaches to structural optimization have now reached a stage where they employ the same basic principles. Indeed, the well-known optimality criteria approach can be viewed as transforming the initial problem in a sequence of simple explicit problems in which the constraints are approximated from virtual work considerations. On the other hand, the mathematical programming approaches have progressively evoluated to a linearization method using the reciprocals of the design variables — this powerful method is proven here to be identical to a generalized optimality criteria approach. Finally, new efficient methods are proposed: (a) a hybrid optimality criterion based on first-order approximations of the most critical stress constraints and zeroth-order approximations of the others and (b) a mixed method which lies between a strict primal mathematical programming method and a pure optimality criteria (or linearization) approach. Simple numerical problems illustrate the concepts established in the paper.     

A unified approach to optimal feature selection

The optimum finite set of linear observables for discriminating two Gaussian stochastic processes is derived using classical methods and distribution function theory. The results offer a new, accurate information-theoretic strategy and are superior to well-known conventional methods using statistical distance measures.