تجزیه و تحلیل حساسیت طراحی و بهینه سازی شکل سازه با مواد فوق الاستیک
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|25531||2000||24 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Computer Methods in Applied Mechanics and Engineering, Volume 187, Issues 1–2, 23 June 2000, Pages 219–243
A continuum-based design sensitivity analysis (DSA) method is developed for structural components with hyperelastic (incompressible) material. A mixed variational principle (MVP) and the total Lagrangian formulation are used for nonlinear analysis. Effects of large displacements, large strains, and material nonlinearities are included in the analysis model, using appropriate kinematics and constitutive relations. The material property and shape DSA using both the direct differentiation method (DDM) and the adjoint variable method (AVM) are discussed. For shape DSA, the material derivative concept is used to compute effects of the shape variation. The boundary displacement and isoparametric mapping methods are employed to compute the design velocity field. Both hydrostatic pressure and structural stiffness are considered as constraints for design optimization, which is carried out by integrating shape design parameterization, design velocity computation, DSA, nonlinear analysis, and the optimization method. Examples such as, an engine mount and a bushing demonstrate the feasibility of the proposed optimization method for designing structural components using hyperelastic material.
Hyperelastic material, such as rubber and rubber-like material, is very versatile and adaptable, and has long been used successfully in numerous engineering applications. Rubber possesses inherent damping, which is particularly beneficial when a resonant vibration is encountered, and it can store more elastic energy than steel. For hyperelastic material, the bulk modulus, which is associated with the volume change of the structural component, is much larger than the shear modulus, which is associated with the shape deformation of the structural component. These properties make the hyperelastic material conducive to a wide range of applications in modern industry, such as weather-stripping for insulation, and bushings and engine mounts for noise, vibration, and harshness (NVH) control. To obtain a meaningful shape optimal design of a hyperelastic solid, it is necessary to accurately describe the material properties, thoroughly understand the nonlinear structural analysis procedure, and to correctly formulate the structural design optimization problem. Many works have been published in the first two areas. For design optimization, DSA, which deals with the effect of change of design variables on the structural response, plays an important role. Various DSA methods for linear structures with sizing and shape design variables have been developed and are well documented ,  and . For nonlinear structures, Choi and Santos , Santos and Choi  and , and Choi  developed sizing and shape DSA methods using the continuum approach. The method was extended to handle geometric nonlinear analysis with linear incompressible material . Using the control volume concept, Tortorelli  developed a DSA method for nonlinear structures with incompressible material. It was shown by Gent that a failure occurs when a structural component with the hyperelastic material comes under a certain hydrostatic tensile stress . On the other hand, the stiffness characteristic is an important design consideration in shape optimal design of the engine mount or bushing for vibration isolation . That is, to reduce the NVH of a vehicle system  and , the optimum design can be obtained using a two-level approach. First, the system level DSA and optimization can be carried out to find optimum gages and topology of the vehicle body, and optimum stiffness and damping characteristics of engine mounts and bushings. In this design formulation, the weight can be considered as the cost, whereas the NVH are treated as design constraints. Once optimum stiffness and damping characteristics of engine mounts and bushings are determined from the system level design, then shapes of engine mounts and bushings can be optimized to yield these stiffness and damping characteristics. The objective of this paper is to develop material property and shape DSA and optimization methods using the continuum approach for hyperelastic structural components. The Mooney–Rivlin energy density function is employed to describe the material property. The FEA code ABAQUS  that utilizes the MVP is used for nonlinear structural analysis. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. For the optimization procedure, the data of shape design parameterization, design velocity computation, nonlinear analysis, and shape DSA are integrated. In this paper, a geometric and finite element model generation tool PATRAN  and VMA Engineering's design optimization tool DOT  are used for design optimization.
نتیجه گیری انگلیسی
A general formulation of DSA for 3-D solids with the hyperelastic material is presented. The MVP is employed to derive material and shape design sensitivity expressions in analytical form. For material property DSA, the coefficients of the Mooney–Rivlin polynomial energy density function are used as design variables. For shape DSA, the boundary displacement and isoparametric mapping methods are used to obtain the design velocity field. Both the AVM and DDM are used to obtain design sensitivity expressions. The tangent stiffness matrix at the final equilibrium configuration of the original design is used in adjoint variable and direct differentiation analysis. The adjoint equation and the direct differentiation equation are linear even though the governing structural equation is nonlinear. In this paper, the Mooney–Rivlin incompressible model of ABAQUS is used for numerical implementation. The design sensitivity coefficient is calculated outside ABAQUS by postprocessing the output data. The DSA methods presented in this research yield accurate design sensitivity information in a computationally efficient manner. The mathematical model of shape design optimization is defined. Due to the material property, the tensile hydrostatic pressure is considered as the failure criterion, and the structural stiffness is chosen as the design requirement. Reasonable optimum designs are obtained for both examples.