Plastic injection molding is one of the most important and major manufacturing methods for plastic products. The process parameters in plastic injection molding affect the quality and the manufacturing cost of plastic products, and it is important to find the optimal process parameters for high quality. But finding optimal process parameters is not easy because the plastic injection molding is nonlinear phenomena. Recently plastic injection molding simulation coupled with optimization technique has attracted attention. In this paper, optimization using a sequential approximate optimization with radial basis function network is adopted to reduce the number of simulation runs. In particular, a multi-objective optimization is formulated. Therefore, both volume shrinkage and clamping force are minimized. In addition, inappropriate process parameters will easily lead to short shot that the melt plastic is not filled into the molding die. In this paper, the short shot is handled as the design constraint. The pareto-frontier is identified with a small number of simulation runs. It is noteworthy that the pareto-frontier is discontinuous. Through numerical simulation, the validity of the proposed approach is discussed.

View full abstract

In deep drawing, area above the trimmed line is called earing. Reduction of the earing in deep drawing is one of the major issues for cost reduction. In addition, a high BHF causes tearing while a low BHF leads to wrinkling. Therefore it is important to determine an appropriate BHF through drawing. Recently, variable BHF (VBHF) approach which varies through the punch stroke has received a lot of attention, and its validity is discussed. In this study, both initial blank shape minimizing the earing and VBHF trajectory are simultaneously determined under tearing/wrinkling constants. Our design problem is formulated as a multi-objective design optimization for evaluation the earing. First objective function is the area above the trimmed line, and second one is the area below the trimmed line. In general, numerical simulation in sheet forming is so expensive that a sequential approximate optimization (SAO) using the radial basis function (RBF) network is adopted to identify the Pareto-frontier. The validity of the proposed approach is examined through numerical simulation. It can be found from the numerical result that earing is drastically reduced by the proposed approach.

View full abstract

The carbon fiber reinforced plastics have been widely used to manufacture the precise structure, such as antenna reflectors, due to their lightweight and high dimensional stability as compared to the metallic materials. When one uses CFRP laminates to antenna reflectors for space telescopes, thermal deformation invokes a serious problem. This deformation can be suppressed if the laminates are stacked symmetrically. It is known, however, that CFRP laminates show unpredictable deformation caused by the ply angle misalignments. Since the ply misalignment is unavoidable, it is important to choose the lay-ups that mitigate the misalignment effects. In this study, the lay-ups and supporting positions are optimized in robust sense by using Taguchi method (TM). Although it is not possible to take into account the effect of interactions between parameters. This is because TM decreases the optimization accuracy in some cases. Therefore, Taguchi method with statistical modeling (TM/S) which considers the interaction effects by using statistical estimated model is proposed. Finally, the performance of TM and TM/S are compared each other.

View full abstract

The advantage of the carbon fiber reinforced plastics (CFRP) is tailoring capability for their mechanical properties by changing the lay-up designs. Recently, meta-heuristic methods (e.g., a genetic algorithm (GA) and a particle swarm optimization (PSO)) have been often employed in such lay-up design problems. In addition to the proper choice among meta-heuristic methods, there are some parameters to be decided carefully to achieve good performance in optimization. In practical problems involving heavy computation costs, however, it is difficult to judge which method is appropriate to a given specific problem and what values are reasonable for the accompanying parameters. In this study, a new benchmark function is proposed to simulate global behaviors of the lay-up design problem and to give criterion for proper choice of the parameters in GA, PSO and the layerwise optimization (LO) methods. In numerical results, performances of the three methods are compared and the proposed benchmark function is shown to be quite effective in simulating the lay-up optimization problem.

View full abstract

In this paper, the structural morphogenesis examples for free-surface grid shell with member of uniform length by genetic algorithms to implement manipulation of decent solution search are indicated. The decent solutions are individuals that have comparatively high evaluation value in the global optimal solution, the local optimal solutions and those neighborhood solutions, we use the genetic algorithm with immune system (ISGA) for the structural optimization procedure that implemented the manipulation of decent solution search. First of all, we indicate the geometric relationship and computational procedure for creating the free-form surface using the Bezier curved surface when the structural members are set to a uniform length. Next, we apply this technique to the structural morphogenesis for a grid shell with the single-objective optimization problem to minimize the total strain energy and the bending strain energy. Finally, the structural properties of these decent solution forms obtained by ISGA are presented.

View full abstract

This paper presents the evaluation method of approximate equivalent stiffnesses for structural optimization of double-skin hollowed plates. For this purpose, the equivalent stiffnesses of the plate are given first in the second-order polynomial form with respect to design parameters by using the Response Surface Method (RSM). Finite element analysis for bending problem is formulated by using the ACM rectangular element, and then FEA program is developed by incorporating the equivalent stiffnesses estimated by RSM. Finally the numerical results by the present FEA are compared with the ones by a commercial FEA code, ANSYS, and the applicability of the approximate equivalent stiffnesses and the present FEA are studied.

View full abstract

In this paper, a parameter-free shape optimization method is presented for designing the optimal free-form of a spatial framed structure. The optimum design problem is formulated as a distributed-parameter shape optimization problem under the assumptions that each member is varied in the out-of-plane direction to the centroidal axis and the cross section is prismatic. Compliance minimization, vibration eigenvalue maximization and displacements control problems are formulated under a volume constraint, and solved as examples of optimal shape design of spatial framed structures. The shape gradient function and the optimality conditions for the problems are then theoretically derived. The optimal free-form is determined by applying the derived shape gradient function to each member as a fictitious distributed force to vary the frame, while minimizing the objective functional. We call this method the H^1 gradient method for frame structures, a gradient method in the Hilbert space. The validity and practical utility of this method are verified through design examples.

View full abstract

The interface shape design of dissimilar materials moves more and more into the field of vision for designers. In the present work, we propose a shape optimization method for designing the interface shape of dissimilar materials consisting of two different materials. The interface boundary between the two different materials is considered as the design boundary for determining the shape of dissimilar materials. The compliance is minimized under the volume constraints of the two materials. Based on the proposed free-form optimization method, we derive the shape gradient function used for minimizing the compliance, and determine the optimal interface shape of dissimilar materials. The numerical results of the given examples show that the proposed free-form optimization method can significantly reduce the compliance of the dissimilar materials.

View full abstract

In the practical design process, uncertainty in the parameters should be appropriately taken into account. In particular, our interest focuses on design problems with dynamic analysis under uncertainty. One of the authors presented a worst-case design of structures based on a random sampling approach, in which constraints are assigned on the worst values of the structural responses. Key concept of the method is estimation of the worst value by Random Search (RS) with order of the function values. Predicting the exact extremes from small samples is difficult in general. Hence, we relax from the worst value to the k-th worst value. Then we can predict and control more accurately the behavior of RS. In two numerical examples, we verify the validity of the estimation by the k-th order statistics. The result indicates use of relatively small samples is enough to predict the large number of future samples even for the noisy and non-smooth dynamic analysis under uncertain parameters.

View full abstract

A stopping rule is presented for multistart local search for optimum design of building frames. The objective function is the total structural volume, and constraints are given for the stresses and interstory drift angles under static loads. The variables representing the sizes of columns and beams are discretized into integer values. The stopping rule is based on the likelihood of existence of undiscovered local optimal solutions, and its performance is investigated using a mathematical problem, for which the number of local optimal solutions are known. Optimization results of a 3-span 6-story frame show effectiveness of the proposed method for terminating the process after finding expected number of local optimal solutions.

View full abstract

Topology optimization on density method on a structural member subject to large inertial force and plastic deformation is discussed. The sensitivities are calculated from the energy difference between two analyses, the current densities and the densities with a slight change for the target element. Maximum energy absorption and load-displacement curve optimization on 1000x100 mm^2 two-dimensional beam subjected to 20 m/s enforced velocity are performed with/without the consideration of inertial force. As a result, the convergence of the objective function are significantly improved and the final topology of the member is different from the one derived from conventional topology optimization method without inertial force.

View full abstract

Structural characteristic like thermal conductivity characteristics and stiffness are affected by structure shape. Shape of material composed structure is also important factor. Thus, material design that is controlled structural characteristic is required. However, artificial design method of materials has not established. As optimal design method, topology optimization has most flexibility among structural optimization. Topology optimization doesn't incident first structure of optimization, and can express internal shape of structure. This research designs optimal shape of material that is hard to occur thermal deformation using topology optimization. Then, this research tries to develop of material that has new structural characteristic in relation to thermal conductivity characteristics and stiffness.

View full abstract

In this paper, we proposed a regularization technique for boundary tracking type level-set topology optimization. This new regularization technique is based on the double-well potential and it realizes smooth convergence in boundary tracking type level-set topology optimization. Because of this regularization technique, boundary tracking type level-set topology optimization is well incorporated with the mathematical programming framework. The usefulness of the proposed regularization technique is demonstrated by solving two numerical examples.

View full abstract

This paper presents a structural optimization method for microstrip components based on topology optimization method. In the proposed method, microstrips are modeled using transition boundary condition of the finite element method. By controlling surface impedance value of the boundary condition locally, it is possible to represent any metallic pattern configuration of microstrip devices on the given design area. Partial diferential equation filtering and Heaviside function projection are utilized with the combination with h-continuation. An design example of coupler-divider composite device on multilayer printed circuit board is provided to illustrate our design approach.

View full abstract

We have been investigating topology optimisation methods with the boundary element method (BEM) and the level set method for wave problems. In this paper, we propose a method for topological sensitivity analysis, which is essential to the topology optimisation method, for two-dimensional elastic wave problems with the BEM. The topological derivative is derived in a regorous manner with the help of the Airy stress function.

View full abstract

This paper presents some topology optimization results for the designs of flow channels of two-dimensional fields. The numerical method is based on the level set method and the lattice Boltzmann method (LBM). Since the LBM is based on an explicit time integration scheme, it can be used efficiently as the numerical method to calculate the flow field repeatedly in the optimization process. In the conventional approach based on the level set method, the optimum results depends on the choice of the regularization parameter value. In the present paper, numerical tests are performed for a square cavity by changing the value of this regularization parameter.

View full abstract