In this paper, the application of orthotropic material orientation optimization for controlling heat flow in electric car power trains is presented. The design process is applied to a case model, which conducts heat while storing heat-sensitive electronic components. The core of the case is designed using a low thermal conductivity material on order to focus the heat flow into the surface layer, which is designed using a high thermal conductivity material. Material orthotropy is achieved in the surface layer of the case by removing the material at points determined by the optimization analysis. For this purpose, an orthotropic material orientation optimization method was extended to calculate optimal material distribution. This is achieved by transforming the initially obtained optimal orientation vector field into a scalar field through the use of coupled time-dependent nonisotropic Helmholtz equations. Multiple parameters allow the control of the scalar field and therefore the control over material distribution in accordance to the optimal orientation. This allows the material distribution pattern to be scaled depending on the desired manufacturing method. The analysis method is applied to divert heat flow from a specific section of the model while focusing the heat flow to another section. The results are shown for a model with a 0.1 mm thick surface layer of copper and are compared to those results from several other materials and layer thicknesses. Finally, the manufactured design is presented.

The object of this study is to clarify wrinkling behavior of a shear-enforced flat rectangular membrane with free boundaries. For this purpose, an equilibrium path tracking method using a finite element method is developed. This method includes bifurcation path tracking analysis that searches for bifurcation solutions. This method establishes an image of membrane behavior by calculating a series of successive equilibrium states before and after bifurcation buckling. Through detailed analysis of stress, displacement fields, and wrinkle interaction over a load parameter range, the analysis shows how existing wrinkles affect each other and the generation of new wrinkles. As a result, there is wrinkle generation with bifurcation and without bifurcation. The wrinkle generation mechanism without bifurcation is analyzed in detail. Wrinkle generation caused by bifurcations could potentially result in a large number of equilibrium paths. Each equilibrium path represents a specific wrinkle pattern. However, the analyzed results show that significantly fewer equilibrium paths are obtained than expected. These are due to wrinkle generation without bifurcations and to deformation symmetry. Nomenclature a = length, m b = width, m D = flexural rigidity, N m 2 E = Young's modulus, GPa f = force, N h = shell thickness, m M = shell section moment, N · m∕m N = shell section force, N∕m q; u = displacement, m t = time, s δf = imposed force, N δu = imposed displacement, m ϵ = membrane strain κ = curvature λ = eigenvalue ν = Poisson's ratio σ = membrane stress, N∕m 2 ϕ = eigenvector

No abstract

This study analyzes wrinkle behavior in both flat and cylindrical membranes undergoing shear displacement. The goal is to establish a relationship between the wrinkle behavior in the two types of membranes and understand how different geometric properties affect the behavior. The analysis is an equilibrium path-tracking analysis using the finite-element method. By applying cyclic boundary conditions to a flat membrane, a degree of similarity in the wrinkle behavior can be established between flat and cylindrical membranes. In both membranes, the initial wrinkles cover the entire membrane. These wrinkles are followed by smaller, localized wrinkles, referred to as collapsed sections. These collapsed sections form on existing wrinkles. The generation of new wrinkles, by splitting the existing wrinkles, is controlled by collapsed sections and is the same in both types of membranes. For the cylindrical membrane, the curved shape results in a more controlled wrinkle behavior. This is represented by fewer bifurcation points that require larger values of shear to occur. Second, the collapsed section frequency and position are fixed with respect to the wrinkle frequency and position. The cause of simplified and controlled wrinkle behavior is analyzed, and the control mechanism is explained. Nomenclature a = length, m b = width, m D = flexural rigidity, N · m 2 d = shell thickness, m E = Young's modulus, GPa f = force, N M = shell section moment, N N = shell section force, N∕m q = displacement, m R = radius, m t = time, s u = displacement, m δf = imposed force, N δu = imposed displacement, m ϵ = membrane strain κ = curvature λ = eigenvalue ν = Poisson's ratio σ = membrane stress, N∕m 2 ϕ = eigenvector

The objective of this study is to clarify the wrinkle behavior of a flat rectangular membrane undergoing shear displacement. To achieve this goal, an equilibrium path tracking method using a finite element method is developed. This method includes a bifurcation path tracking analysis that searches for bifurcation solutions. This method establishes an image of the membrane behavior by calculating a series of successive equilibrium states before and after bifurcation buckling. Generally in experiments, flat rectangular membranes have shear displacement imposed on top or bottom edges, while the left and right sides have free boundaries. At large values of shear displacement, the wrinkles cover the entire membrane, but the free boundaries result in uneven shapes and distributions. Further increase in shear results in small wrinkles, referred to as collapsed sections, generated on existing wrinkles. As collapsed sections grow, new wrinkles are generated. However, the universality of this wrinkle generation mechanism may be affected by the free boundaries. By applying cyclic boundary conditions, effects of free boundaries, which include uneven wrinkle shape and distribution, can be eliminated. In addition, by changing the membrane aspect ratio, the effects of geometry are also evaluated. For all membranes, the wrinkle generation from collapsed sections is observed and its independence from free boundaries and aspect ratio is shown. By analyzing stress and displacement fields, the formation of collapsed sections is explained. In addition, for the cyclic boundary conditions, the change in aspect ratio results in almost the same bifurcation structure. Therefore, the wrinkle behavior evaluation in this study can be useful in predicting wrinkle behavior.