Shape Sensitivity Formulation for Axisymmetric Thermal Conducting Solids

1993 ◽  
Vol 207 (3) ◽  
pp. 209-216 ◽  
Author(s):  
Boo Youn Lee
Keyword(s):  
Shape Change ◽  
Direct Method ◽  
Design Sensitivity ◽  
Boundary Integral ◽  
Singular Boundary ◽  
Concept Design ◽  
Shape Sensitivity ◽  
Material Derivative ◽  
Thermal Conducting ◽  
Thermal Diffuser

A direct differentiation method is presented for the shape design sensitivity analysis of axisymmetric thermal conducting solids. Based purely on the standard boundary integral equation (BIE) formulation, a new BIE is derived using the material derivative concept. Design derivatives in terms of shape change are directly calculated by solving the derived BIE. The present direct method has a computational advantage over the adjoint variable method, in the sense that it avoids the problem of solving for the adjoint system with the singular boundary condition. Numerical accuracy of the method is studied through three examples. The sensitivities by the present method are compared with analytic sensitivities for two problems of a hollow cylinder and a hollow sphere, and are then compared with those by finite differences for a thermal diffuser problem. As a practical application to numerical optimization, an optimal shape of the thermal diffuser to minimize the weight under a prescribed constraint is found by use of an optimization routine.

Boundary Formulations for Three-Dimensional Continuum Structural Shape Sensitivity Analysis

1992 ◽  
Vol 59 (4) ◽  
pp. 827-834 ◽  
Author(s):  
J. H. Kane ◽  
G. Zhao ◽  
H. Wang ◽  
K. Guru Prasad
Keyword(s):  
Sensitivity Analysis ◽  
Three Dimensional ◽  
Structural Response ◽  
Surface Displacement ◽  
Design Sensitivity ◽  
Singular Boundary ◽  
Shape Sensitivity ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Structural Shape

The direct, singular, boundary element analysis formulation is shown to provide a basis for a computationally efficient and accurate shape design sensitivity analysis approach for the structural response of three-dimensional solid objects. The theoretical formulation for surface displacement and traction component sensitivities, and all components of the stress tensor is presented along with a formulation for the recovery of displacement and stress components in the interior of the object under consideration. Discussion of computational issues related to the overall efficiency of these formulations is given, along with numerical results to demonstrate the accuracy and efficiency of this approach.

scholarly journals Modelling Nuclear Morphology and Shape Transformation: A Review

Membranes ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 540
Author(s):  
Chao Fang ◽  
Jiaxing Yao ◽  
Xingyu Xia ◽  
Yuan Lin
Keyword(s):  
Shape Change ◽  
Boundary Integral ◽  
Shape Transformation ◽  
Cellular Processes ◽  
Physical Mechanisms ◽  
Intracellular Forces ◽  
Cellular Compartments ◽  
Progeria Syndrome ◽  
Hutchinson Gilford Progeria Syndrome ◽  
Made In

As one of the most important cellular compartments, the nucleus contains genetic materials and separates them from the cytoplasm with the nuclear envelope (NE), a thin membrane that is susceptible to deformations caused by intracellular forces. Interestingly, accumulating evidence has also indicated that the morphology change of NE is tightly related to nuclear mechanotransduction and the pathogenesis of diseases such as cancer and Hutchinson–Gilford Progeria Syndrome. Theoretically, with the help of well-designed experiments, significant progress has been made in understanding the physical mechanisms behind nuclear shape transformation in different cellular processes as well as its biological implications. Here, we review different continuum-level (i.e., energy minimization, boundary integral and finite element-based) approaches that have been developed to predict the morphology and shape change of the cell nucleus. Essential gradients, relative advantages and limitations of each model will be discussed in detail, with the hope of sparking a greater research interest in this important topic in the future.

Design Sensitivity Analysis for the Meshfree Shell Structure

2001 ◽  
Author(s):  
Kyung K. Choi ◽  
Nam H. Kim ◽  
Mark E. Botkin
Keyword(s):  
Sensitivity Analysis ◽  
Shell Structure ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Analysis Method ◽  
Sensitivity Equation ◽  
Material Derivative ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Shell Formulation

Abstract A unified design sensitivity analysis method for a meshfree shell structure with respect to sizing, shape, and configuration design variables is presented in this paper. A shear deformable shell formulation is characterized by a CAD connection, thickness degeneration, meshfree discretization, and nodal integration. The design variable is selected from the CAD parameters, and a consistent design velocity field is then computed by perturbing the surface geometric matrix. The material derivative concept is used to obtain a design sensitivity equation in the parametric domain. Numerical examples show the accuracy and efficiency of the proposed design sensitivity analysis method compared to the analytical solution and the finite difference solution.

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