Y-stiffened panel multi-objective optimization using genetic algorithm

Optimization of a fender structure for the crashworthiness design

Various optimization problems have been studied for the purpose of structural morphogenesis by many researchers. Structural optimization problems can be classified into three different sub-problems, namely size, shape and topology optimization problem. Size optimization problem is consisted of small sets of design variables. The shape and topology of a structure are defined by a set of design variables, and these design variables are adjusted to achieve given objectives, such as minimum volume. Such optimization problems can be solved iteratively, using gradient-based techniques. Introducing more design variables increases the complexity of the optimization problem. Therefore, it becomes difficult to solve the optimization problem by using MP techniques with large sets of design variables. Heuristics can be improved the difficulty. There are many studies using heuristics like genetic algorithm and simulated annealing. An effective method for structural morphogenesis inspired by self-organization phenomena is presented in this paper. Self-organization is a phenomenon that an entire structure gradually emerges by interaction between elements of the structure, and the elements are affected by the entire structure. Since the self-organization algorithm consists of simple calculation iteration, it can be applied to problems with large number of design variables. Proposed method is applied to problems of uniform member length, minimization of strain energy and cross-section design for frame structures, and the effectiveness is demonstrated through some examples. On the other hand, the number of projects incorporating computational design has increased in recent year, and designs with complicated forms composed of free surfaces are also increasing. In order to design such a shape, the designer needs to consider the rationality of the structure from the initial stage. So, it seems necessary to develop simple software for the structural morphogenesis. Therefore, we developed components of Grasshopper that works within Rhinoceros, so that it will be possible to reassemble algorithms in an intuitive way for designers who have never experienced programming. Grasshopper is one of Graphical Algorithm Editor (GAE), and can be visually constructed an algorithm by connecting components that is a function of modeling. Analysis by gradient-based MP techniques often involves jumping of solutions and analytical instability peculiar to non-linear problems, and it is difficult to apply to the computer aided systems as described above. Analysis algorithms based on self-organizing algorithms are considered to be suitable for the above system due to their high robustness.

This paper presents an extension of fuzzy-multi-objective genetic algorithm (MOGA) optimization methodology that could effectively be used to find the overall satisfaction of objective functions (selecting the design variables) in the early stages of design process. The coupling of objective functions due to design variables in an engineering design process will result in difficulties in design optimization problems. The primary application of this methodology is the design of a liquid propellant engine with the maximum specific impulse and the minimum weight. The independent design variables in this model are combustion chamber pressure, exit pressure, oxidizer to fuel mass flow rate. To handle the mentioned problems, a fuzzy-multi-objective genetic algorithm optimization methodology is developed based on Pareto optimal set. Liquid propellant engine, F-1 is modeled to illustrate accuracy and efficiency of proposed methodology.

Designing a drive train for an industrial robot is a demanding task where a set of design variables need to be determined so that optimal performance is obtained for a wide range of different duty cycles. The paper presents a method where singular value decomposition (SVD) is used to reduce the design variable set. The application is a six degree of freedom serial manipulator, with nine drive train parameters for each axis and the objective is to minimize the cycle time on 122 representative design cycles without decreasing the expected lifetime of the robot. The optimization is based on a simulation model of the robot and conducted on a reduced set of the initial duty cycles and with the design variables suggested by the SVD analysis. The obtained design reduces the cycle time with 1.6% on the original design cycles without decreasing the life time of the robot.

Integrated structural and control optimization of intelligent structures

A method is presented to integrate the design space for structural/control system optimization problems in the case of linear state feedback control. Nonstructural lumped masses and control system design variables as well as structural sizing variables are all treated equally as independent design variables in the optimization process. Structural and control design variable linking schemes are used in order to avoid a prohibitively large increase in the total number of independent design variables. When actuator masses are treated as nonstructural lumped mass design variables, special consideration is given to the relation between the transient peak responses and the required actuator masses which is formulated as a behavior constraint form. The original nonlinear mathematical programming problem based on a finite element formulation and linear state feedback is replaced by a sequence of explicit approximate problems exploiting various approximation concepts such as design variable linkings, temporary constraint deletion and first order Taylor series expansion of nonlinear behavior constraints in terms of intermediate design variables. Examples which involve a variety of dynamic behavior constraints (including constraints on closed-loop eigenvalues, peak transient displacements, peak actuator forces, and relations between the peak responses and the actuator masses) are effectively solved by using the method presented.

This paper gives a short review of real coded genetic algorithm (RCGA) used for multiobjective optimization. Handling of continues search space is very easy with RCGA and solution representation is very close to natural formulation of real-world problems. Because of the obvious reasons, most of real-world multi-objective optimization problems are solved using RCGA. The topics discussed in this paper include new algorithms, design issues of multi-objective optimization like efficiency, scalability, constraint handling and self-adaptation. This discussion suggests potential areas for future research, namely, design of new algorithm, new recombination operator and Pareto optimal front formation techniques.

Many real-world design problems involve simultaneous optimisation of multiple objectives. The considered grillage design is a multi-objective optimisation problem since there are two objective functions, namely: the volume design and the cost design. Thus, the solution of this optimisation problem requires specialised method suitable for multi-objective problems. In this article, a multi-objective design optimisation using real-coded genetic algorithm is proposed for the Pareto-optimality of grillage system. The objective functions in the optimisation problem measure the design sensitivities in grillage system. The non-linear constrained multi-objective optimisation is very important from the point of view of practical problem solving. Therefore, the real-coded genetic algorithm with multiple genetic operators is proposed to find the optimum grillage system without handling any of the penalty functions. Direct strength calculation defined from the class rules of DNV was applied for structural design of grillage system. The hybrid method (real-coded genetic algorithm including the non-dominated sorting and sharing approaches) performs a marvellous explorability in finding a diverse set of solutions and in converging near the true Pareto-optimal set. The results obtained are very encouraging since they show that we can produce an important portion of the Pareto-front at a very low computational time frame.

Objectives: This nonlinear three-dimensional finite element analysis (FEA) study evaluated the effect of the number of implants, distal implant inclination, and use of angled abutments on stress magnitude and distribution in cortical bone (CB), abutment screw (AS), and prosthetic screw (PS) of implant-supported fixed complete dentures. Methods: Nonlinear 3D FEA models of mandibular fixed complete dentures were created with five, four, or three parallel straight implants (5S, 4S, 3S) and with tilted distal implants (5T, 4T, 3T). In addition, the 5T model was tested using angled abutments over the tilted distal implants to re-align the implant inclination. A 100-N axial load was applied over the first molar region (cantilever) to analyze the von Mises stresses in selected points (CB, AS, and PS). Results: The implant adjacent to the load showed the highest stresses in CB, AS, and PS. The model with three implants showed higher stresses than the ones with four and five implants. Peak stresses in the AS increased 40% from five to four implants and 100% from five to three implants. Tilting the distal implants increased stresses in CB. Peak stress in the PS increased 150% from 5S to 5T models and 100% from 4S to 4T models. Angled abutments generated lower stresses on CB and AS but higher stresses on PS. Conclusions: The results suggest that stresses in the cortical bone, abutment screw, and prosthetic screw increase when tilting the posterior implants and reducing the number of implants. The use of angled abutments decreased stresses at the bone-implant interface and in abutment screws but increased stresses on prosthetic screws.

This paper deals with joint penalization and material selection in frame topology optimization. The models used in this study are frame structures with flexible joints. The problem considered is to find the frame design which fulfills a stiffness requirement at the lowest structural weight. To support topological change of joints, each joint is modelled as a set of subelements. A set of design variables are applied to each beam and joint subelement. Two kinds of design variables are used. One of these variables is an area-type design variable used to control the global element size and support a topology change. The other variables are length ratio variables controlling the cross section of beams and internal stiffness properties of the joints. This paper presents two extensions to classical frame topology optimization. Firstly, penalization of structural joints is presented. This introduces the possibility of finding a topology with less complexity in terms of the number of beam connections. Secondly, a material interpolation scheme is introduced to support mixed material design.

The Method of Imprecision (MOI) is a multi-objective design method that maximizes the overall degree of both design and performance preferences. Sets of design variables are iteratively selected, and the corresponding performances are approximately computed. The designer’s judgment (expressed as preferences) are combined (aggregated) with the customer’s preferences, to determine the overall preference for sets of points in the design space. In addition to degrees of preference for values of the design and performance variables, engineering design problems also typically include uncertainties caused by uncontrolled variations, for example, measuring and fabrication limitations. This paper illustrates the computation of expected preference for cases where the uncertainties are uncorrelated, and also where the uncertainties are correlated. The result is a “best” set of design variable values for engineering problems, where the overall aggregated preference is maximized. As is illustrated by the examples shown here, where both preferences and uncontrolled variations are present, the presence of uncertainties can have an important effect on the choice of the overall best set of design variable values.

In this paper we develop an as-yet-missing theoretical framework as well as a general methodology for model-based robust design. At the outset, a distinction is made between three sets: the set of design variables, grouped in the n-dimensional vector x, which are to be assigned values as an outcome of the design job; the set of design-environment parameters (DEP), grouped in the v-dimensional vector p, over which the designer has no control; and the set of performance functions, arrayed in the m-dimensional vector f, representing the functional relations among performance, design variables and DEP. Resorting to the mathematical model available for the object under design, an m × v design performance matrix F, mapping the space of relative variations of p into that of relative variations of f, is derived. Moreover, two pertinent concepts are introduced: the design sensitivity matrix, which plays a major role in the transmission of the variations of p into variations off, and its associated bandwidth, defined as the logarithm of the square root of the ratio between the maximum to the minimum singular values of the design performance matrix, measured in decades. A result stating the relation between the bandwidth of a matrix and its inverse is shown. Consequently, the aforementioned bandwidth represents an index for evaluating the robustness of a design. To demonstrate our approach, case studies are included

Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper explains how 9 5/8" turbine diamond bit designs for the North Sea were optimized through the combined results of practical field developments and analytical practical field developments and analytical design studies. Various mechanical characteristics such as bit face contour, diamond size, and diamond pattern were analyzed with the aid of the diamond drilling theory, taking into account the particular conditions encountered in North Sea drilling. The mathematical model for rotary and turbine diamond drilling as used in this study was developed during recent years, and is now considered an effective aid to design optimization. The drilling theory is based on previously reported studies on the cutting actions of single diamonds in rocks, now expanded to encompass the total effect of all diamonds on the cutting surfaces of the bit. Using specific drilling conditions and rock properties, expressions for bit torque, properties, expressions for bit torque, penetration rate, rotary power and other penetration rate, rotary power and other performance characteristics are obtained in performance characteristics are obtained in terms of bit weight, rotary speed and the design parameters, like diamond size, fluid handling characteristics and geometric factors. The evolution of the bit designs leads to a bit style which, within the known limitations on diamonds, has best theoretical performance and best field performance. Introduction In view of the expanding use and importance of turbo diamond drilling techniques, particularly in modern offshore development, particularly in modern offshore development, it is important to study the way in which diamond bits work under the specific conditions imposed by turbines, and to use this knowledge to improve the performance of the diamond tools. In this study, several practical turbo diamond bit design approaches are practical turbo diamond bit design approaches are studied analytically in an effort to isolate the best performing or "optimum" combination of bit design variables. The goal of optimization is to find the particular set of design variables which yields the highest penetration rate under the selected operating conditions, without violating any of the assumed practical limitations on loading and application of the diamonds, the diamond bits and the turbines.

Aircraft manufacturing companies have to consider multiple derivatives to satisfy various market requirements. They modify or extend an existing aircraft to meet new market demands while keeping the development time and cost to a minimum. Many researchers have studied the derivative design process, but these research efforts consider baseline and derivative designs together, while using the whole set of design variables. Therefore, an efficient process that can reduce cost and time for aircraft derivative design is needed. In this research, a more efficient design process is proposed which obtains global changes from local changes in aircraft design in order to develop aircraft derivatives efficiently. Sensitivity analysis was introduced to remove unnecessary design variables that have a low impact on the objective function. This prevented wasting computational effort and time on low priority variables for design requirements and objectives. Additionally, uncertainty from the fidelity of analysis tools was considered in design optimization to increase the probability of optimization results. The Reliability Based Design Optimization (RBDO) and Possibility Based Design Optimization (PBDO) methods were proposed to handle the uncertainty in aircraft conceptual design optimization. In this paper, Collaborative Optimization (CO) based framework with RBDO and PBDO was implemented to consider uncertainty. The proposed method was applied for civil jet aircraft derivative design that increases cruise range and the number of passengers. The proposed process provided deterministic design optimization, RBDO, and PBDO results for given requirements.

The design shear resistance of an existing structure can be evaluated with analytical design procedures and numerical procedures provided by non‐linear finite element analyses. The new fib Model Code 2010 proposes different calculation methods that fall into four different levels of approximation. As the level of approximation rises, so the complexity and the accuracy of the calculated shear resistance increases. Non‐linear finite element analyses belong to the highest level of approximation, but although they are more and more becoming a customary tool in the daily design process, building codes do not provide guidance on how to perform these analyses.This paper describes non‐linear finite element analyses performed on prestressed beams, which underwent shear failure during experimental loading, in order to assess and criticize the finite element approaches. The aim of this work is to propose guidelines for numerical simulations in order to reduce model and user factors. The results obtained from the non‐linear finite element analyses have been compared with the analytical results using different levels of approximation. The design shear resistance obtained with the highest level of approximation, level IV, derived from non‐linear finite element analyses, turned out to be higher than the design shear resistance obtained with analytical procedures (levels I/II/III).