Optimal Thickness Distribution Research Articles

Design of Heat Conduction Panel: The Case of Multiple Heating Elements Cooled by a Displaced Heat Sink

This paper reports the design study performed on a heat conduction panel having several heat sources at separate locations and a heat sink on one of the panel corners. The panel is given a thickness distribution so as to provide spatially varying heat conduction paths from the heat sources to the heat sink. The objective of thickness distribution design is to reduce the variation among heat source temperatures and the maximum heat source temperature simultaneously. The genetic algorithm is used to search for an optimum thickness distribution. The problem is a generic representation of the situations that are becoming common in a compact electronic equipment.

Design and Optimisation of a Blow Moulded Container

This work is focused on the first step of the extrusion blow moulding process as part of a global optimisation process encompassing several steps: optimisation of the part thickness, optimisation of the parison thickness that will guarantee the specified thickness profile and optimisation of the extrusion conditions (namely, the sequence of the die mandrel movements) required to obtain the optimal parison thickness distribution. A high density polyethylene (HDPE) extrusion blow moulded tamper evident container was studied using a finite element based analysis (FEA) in order to determine the optimized thickness distribution required for the blown part, considering its mechanical specifications. Several tests corresponding to the requirements for UN homologation for dangerous substances transportation were performed using a commercial software. Non-linear models were used to better describe the mechanical part behaviour. The results obtained at this stage were used to redesign the blown part. In future work this optimised design will be used as an input for optimising the subsequent stages.

Thickness optimization of a multilayered structure on the coupling surface between a structure and an acoustic cavity

This paper describes a new design method to optimize thickness distribution of a multilayered structure which is located on the coupling surface between a structure and an acoustic cavity. The design method is based on the concept of the density approach in topology optimization incorporating a transfer matrix for a multilayered structure that includes a poroelastic media layer. The one-dimensional transfer matrix adopted here is an approximate representation addressing vibro-acoustic effects inherent in a multilayered structure, and balances calculation resources and desired accuracy. Applying the transfer matrix representation as boundary conditions on the coupling surface between a structure and an acoustic cavity, the modified equilibrium equation of the vibro-acoustic system is derived which is approximately but efficiently solved by the modal approach. In this study, the problem of minimizing the acoustic pressure within the cavity over the prescribed frequency range is formulated under the volume constraint of the poroelastic media layer. The continuous approximation of thickness distribution is assumed, and the thickness of the poroelastic media layer at each nodal point is chosen as design variables. Numerical results show that an acoustic response is significantly reduced by the optimal thickness distribution having a total weight equal to or less than that in the initial uniform thickness. These demonstrate that the proposed method is effective to design the optimal thickness distribution of a multilayered structure.

インフレータブルリフレクタ膜の最適膜厚

The purpose of this paper is to obtain an optimum thickness distribution of an inflatable membrane reflector which consists of two circular membranes attached at their edges. The deflection analysis of the membrane is based on the large deflection theory of plate. In numerical simulation, the finite element method is used. In the optimization, the objective function is the surface profile error between the paraboloid and the inflated shape of membrane, and the discrete distribution of optimum thickness is obtained. In addition, the simulation for experiment is performed under a restricted condition in thickness. Based on this result, a circular membrane with optimized thickness profile is produced and the shape measurement experiment is performed.

Optimum Aeroelastic Design of a Flapping Wing

A method is presented for the optimum aeroelastic design of a flapping wing employing a lifting-surface theory as an aerodynamic tool and the complex method as the optimization algorithm. The method is applied to the optimum design of a flapping wing of a Kite Hawk (Milvus migrans) unmanned air vehicle and the optimum thickness distribution of the main spar is determined. As a result of the optimization, a high propulsive efficiency of 75% is attained considering only dihedral flapping of the main spar. By evaluating the viscous effect for this optimum design using a three-dimensional Navier-Stokes code, the effectiveness of the design is confirmed.

Thickness Optimization for Multilayered Structures Located on the Coupling Surface Between a Structure and an Acoustic Cavity

This paper describes a new design method for optimizing the thickness distribution of a multilayered structure located on the coupling surface between a structure and an acoustic cavity. The design method is based on the concept of a topology optimization method incorporating a transfer matrix for the multilayered structure that includes a poroelastic media layer. The one-dimensional transfer matrix adopted here is an approximate representation addressing vibro-acoustic effects inherent in a multilayered structure over a range of low frequencies, and balances calculation times and desired accuracy. In this study, the problem of minimizing the acoustic pressure within the cavity over the prescribed frequency range is formulated under the constraint of the total weight of the design domain. The thickness of the poroelastic media layer at each nodal point is chosen as the design variables. Numerical results show that acoustic response is significantly reduced by an optimal thickness distribution having a total weight equal to or less than that of the initial thickness.

Optimizing parison thickness for extrusion blow molding by hybrid method

Abstract A hybrid method consisting of finite element method (FEM), artificial neural network (ANN), and genetic algorithm (GA) was used to find the optimal parison thickness distribution for a blow molded part with required thickness distribution. Firstly, numerical simulations on the parison inflation were performed using FEM and the K-BKZ integral type constitutive equation. Based on the simulation results, a back propagation (BP) ANN model was then developed to build the relationship between parison thickness distribution and the objective function, which was used to evaluate the wall thickness distribution of part. The predictive ability of the ANN model was verified through FEM simulation results different from those utilized in the training stage. Finally, a GA was developed and used to search for the optimal parison thickness distribution. The results showed that the hybrid method proposed in this work can effectively obtain the optimal parison thickness distribution for a blow molded part with required wall thickness distribution. Compared with the trial and error method, the hybrid method can shorten the part development time and save a lot of material.

Finite Element and Neural Network Modeling of Viscoelastic Annular Extrusion

Plastics blow molding has grown rapidly for the past couple of decades. Annular parison extrusion is a critical stage in extrusion blow molding. In this work, numerical simulations on the parison extrusion were performed using finite element (FE) method and the Kaye-Bernstein-Kearsley-Zapas type constitutive equation. A total of 100 simulations was carried out by changing the extrusion die inclination angle, die gap, and parison length. Then a backpropagation artificial neural network (ANN) was proposed as a tool for modeling the parison extrusion using the numerical simulation results. The network architecture determination and the training process of the ANN model were discussed. The predictive ability of the ANN model was examined through several sets of FE simulation results different from those utilized in the training stage. The effects of the die inclination angle, die gap, and parison length on the parison swells can be predicted using the ANN model. The results showed that the die gap has a smaller effect on the diameter swell but a greater effect on the thickness swell. Both diameter and thickness swells increase as the die inclination angle increases. The hybrid method combining the FE and ANN can shorten the time for the predictions drastically and help search out the processing conditions and/or die geometric parameters to obtain optimal parison thickness distributions.

Superplastic forming of bellows expansion joints made of titanium alloys

Abstract A new forming technology was developed for bellows expansion joints. This technology uses superplastic forming (SPF) method of applying gas pressure and compressive axial load. It is developed and can be used to manufacture large diameter “U” type bellows expansion joints made of titanium alloys. The forming technology for bellows expansion joints made of titanium alloys is presented to make a two-convolution bellows expansion joint of Ti–6Al–4V alloy as an example. Welded pipe bent by a hot bending method with a set of specific dies and welded by plasma arc welding was used as a tubular blank in the SPF. During the SPF process the tubular blank is restrained in a multi-layer die block assembly which determines the final shape of convolution. The forming load route is divided into three steps in order to obtain optimum thickness distribution. This technology can also be used to fabricate stainless steel bellows expansion joints.

Research on Structural Optimization Technique by CA changing Majority Rule

The structural optimization problems consist of phase optimization and size optimization steps. The size optimization is comparatively easily using a mathematical technique, but the more important phase optimization is difficult. Until now, researches using GA, NN, SA and CA as the phase optimization technique are done. In this paper, “the method by CA changing majority rule” is proposed. It is the method searching an optimal structure without increasing a design variable and keeping design space large. Moreover this method makes the operation from phase determination to size decision systematically. By using the method, the design problems of the optimum board thickness distribution are analyzed as an exercise about the validity

Optimal design of an electrostatically actuated microbeam for maximum pull-in voltage

We consider optimizing the shape of a capacitive micro-beam for maximum pull-in voltage. The problem is discretized using finite elements. The normal flow algorithm is used to trace the nonlinear voltage displacement curve and find the pull-in point. Optimal width and thickness distributions are obtained for different beam boundary conditions using a resizing scheme based on optimality criterion. The results indicate that substantial increase in pull-in voltage can be achieved by varying the width and/or thickness distribution.

225 超音速フラッタ特性と構造質量を同時に考慮した平板翼の多目的複合領域構造最適化

This paper investigates the properties of the optimum structural design for supersonic flutter of the plate wing. The optimization method is based on the Evolutionary Structural Optimization method. In order to consider the properties of the optimum structural design, the optimum mass distribution, the optimum stiffness distribution and the optimum equivalent thickness distribution are compared in the numerical experiments. Numerical results show that the equivalent thickness distribution is the most suitable for the design variable of the structural optimization for the supersonic flutter. Numerical results also show that the optimum stiffness distribution has a relationship with the strain energy density of the 2nd flutter mode shape near the critical dynamic pressure.

Optimum Flagellum Shape of a Micromachine Imitating a Microorganism.

The purpose of the present study is to develop micromachines imitating flagellated micro-organisms. The speed of advance, the radius of trajectory and the power consumption of a micromachine are computed by using the boundary element method to optimize seven parameters that express the shape of an actual microorganism and six parameters that stand for the flagellum shape of a micromachine. The optimum cross-sectional shape of the flagellum is an ellipse which is somewhat inclined with respect to the principal normal line of the flagellum spiral. The optimum thickness distribution of the flagellum is such that the position of maximum thickness is very close to the head of the machine. The optimization leads to the reduction of power consumption by 22 percent compared with the power consumed by the actual microorganism.

Study on Optimum Structural Design using Evolutionary L system.

Lsystem (LS) is a technique expressing a formation algorithm creating the various shape patterns by the simple rules. Using LS, the complex branch phenomena of plants could be described by simple rules. This paper has tried the methodology to apply LS to the structural design. This methodology grows up the structure as if plants grow up, and produces the optimum structure that is appropiate for the design purpose. It is difficult to acquire LS rules for the optimum structure because the rules have many degrees of freedom. Therefore, this paper proposes an idea that evolves LS rules using Genetic Algorithms (GA) . The methodology is called as an evolutionary LS (ELS) . Using the methodology, the design problems to decide optimum distribution of material and plate thickness are solved.

Dangers inherited in shells optimized with linear assumptions

Abstract This paper provides the background theory and results of an investigation into the dangers inherited in the shells optimized using linear elastic, small displacement, Reissner–Mindlin shell models with shape and/or size design variables. The various tools developed and utilized in this study are briefly described and include computational geometric modelling, automatic mesh generation, finite element analysis, design sensitivity analysis and mathematical programming procedures. In the subsequent studies, once the optimal shape and thickness distributions of the shell have been determined, the non-linear buckling loads of the initial and optimized shells are investigated using a geometrically non-linear analysis tool capable of dealing with complex load–displacement paths including snap-through and snap back.

Ideal stretch forming for minimum weight axisymmetric shell structures

A companion paper “Minimum Weight Design of Axisymmetric Shell Structures” by Richmond and Azarkhin describes the design of axisymmetric thin-walled structures and parts that can support specified loads with minimum material. The result is an optimum shape and thickness distribution in the final part when the strength of the material is assumed to be uniform. Here, we demonstrate the application of ideal forming theory to design sheet stretching processes that can produce the optimum shapes and thickness distributions from flat sheets of uniform thickness. Specific designs are achieved for producing minimum weight shell structures that will support a specified uniform pressure assuming both the Mises and the Tresca yield criteria along with the rigid-perfectly plastic flow condition. In the case of the Tresca yield condition, the optimum structure is a spherical shell segment with uniform thickness, and an associated ideal stretching process is hydraulic bulging. Because the effects of strain hardening have been neglected in the structural optimization theory, it has been possible here to design the minimum weight structure and its forming process sequentially. In subsequent work, we plan to include the effects of strain hardening on the shell strength, which will then require coupled design of the structure and its forming process. Also extension of these methods to three-dimensional geometries will be considered.

異なる板厚形状を有する７４７５アルミニウム合金板材の超塑性ブロー成形

A new superplastic blow forming procedure for 7475 aluminum alloy sheets to provide the optimum distribution of thickness to a slender pan. The procedure adopts a preliminarily machined blank with different thickness locally before a superplastic forming (SPF). The figure and thickness for machining is calculated by a numerical analysis method developed for the pan to be formed with the optimum shape, size and thickness. This procedure also contains a friction between a sheet and a die, and work hardening of a blank material during SPF. It feeds the optimum pressurization schedule to the preliminarily machined blank to be formed with the maximum strain rate. A SPF of 7475 aluminum alloy sheets machined preliminarily to be formed a rectangular pan, in the ratio of the bottom to wall thickness is 2:1, according to the numerically calculated pressurizing schedule. The distribution of thickness in the formed pan was coincident with that of expected one.

Improvement of thickness distribution and crystallinity of ZnO thin films prepared by radio frequency planer magnetron sputtering

An improvement of thickness distribution and crystallinity in ZnO thin films prepared by radio frequency (rf) planer magnetron sputtering have been studied. Optimum thickness distribution of less than ±2.2% in a 3-inch wafer is obtained by changing the substrate angle to the ZnO target and is in accordance with cosine law. C -axis orientation perpendicular to the silicon substrate is confirmed by X-ray diffraction. The stress of ZnO thin films is more than 0.3 GPa and its distribution is independent of the substrate angle that is set at a slant to the optimum angle for thickness distribution. These results indicate that thickness distribution of ZnO thin films heavily depends on the substrate angle, while the c -axis orientation, the stress and its distribution are independent of the setting angle of the substrate. The stress distribution is attributed to the lattice constant distribution and the crystallinity distribution of ZnO thin films.

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.

Internal Stress of ZnO thin Films Caused by Thickness Distribution and Crystallinity

AbstractThe improvement of thickness distribution and crystallinity in ZnO thin films prepared by radio frequency (rf) planer magnetron sputtering has been studied. Optimum thickness distribution of less than ± 2.2% in a 3-inch wafer is obtained by changing the substrate angle to the ZnO target and is in accordance with cosine law. The c-axis orientation perpendicular to the silicon substrate is confirmed by x-ray diffraction. The stress of ZnO thin films is larger than 0.3GPa and its distribution is independent of the substrate angle that is set at a slant to the optimum angle for thickness distribution. These results indicate that thickness distribution of ZnO thin films heavily depends on the substrate angle, while the stress and its distribution are independent of the setting angle of the substrate. Stress distribution is attributed to the distribution of argon ions and sputtered molecules impinging a wafer.