Discussion on the optimality condition of the equivalent static loads method for linear dynamic response structural optimization

2018 ◽  
Vol 59 (1) ◽  
pp. 311-316
Author(s):  
Gyung-Jin Park ◽  
Youngmyung Lee
Keyword(s):  
Dynamic Response ◽  
Structural Optimization ◽  
Optimality Condition ◽  
Static Loads ◽  
Linear Dynamic ◽  
Equivalent Static Loads ◽  
Equivalent Static Loads Method

Non-linear dynamic response structural optimization for frontal-impact and side-impact crash tests

2016 ◽  
Vol 231 (5) ◽  
pp. 600-614 ◽  
Author(s):  
Youngmyung Lee ◽  
Gyung-Jin Park
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Structural Optimization ◽  
Side Impact ◽  
Static Response ◽  
Static Loads ◽  
Linear Dynamic ◽  
Equivalent Static Loads ◽  
Non Linear ◽  
Equivalent Static Loads Method

Vehicle crash optimization is a representative non-linear dynamic response structural optimization that utilizes highly non-linear vehicle crash analysis in the time domain. In the automobile industries, crash optimization is employed to enhance the crashworthiness characteristics. The equivalent-static-loads method has been developed for such non-linear dynamic response structural optimization. The equivalent static loads are the static loads that generate the same displacement field in linear static analysis as those of non-linear dynamic analysis at a certain time step, and the equivalent static loads are imposed as external loads in linear static structural optimization. In this research, the conventional equivalent-static-loads method is expanded to the crash management system with regard to the frontal-impact test and a full-scale vehicle for a side-impact crash test. Crash analysis frequently considers unsupported systems which do not have boundary conditions and where adjacent structures do not penetrate owing to contact. Since the equivalent-static-loads method uses linear static response structural optimization, boundary conditions are required, and the impenetrability condition cannot be directly considered. To overcome the difficulties, a problem without boundary conditions is solved by using the inertia relief method. Thus, relative displacements with respect to a certain reference point are used in linear static response optimization. The impenetrability condition in non-linear analysis is transformed to the impenetrability constraints in linear static response optimization.

Dynamic response optimization of structures with viscoelastic material using the equivalent static loads method

2020 ◽  
pp. 095440702095712
Author(s):  
Sang-ok Park ◽  
Wook-Han Choi ◽  
Gyung-Jin Park
Keyword(s):  
Dynamic Response ◽  
Structural Optimization ◽  
Dynamic Analysis ◽  
Viscoelastic Material ◽  
Optimization Method ◽  
Objective Functions ◽  
Static Loads ◽  
Equivalent Static Loads ◽  
Equivalent Static Loads Method ◽  
Response Optimization

Viscoelastic material is widely used in automotive structures due to its outstanding vibration-damping characteristics with appropriate stiffness. Viscoelastic material, which has viscosity and elasticity, shows energy absorption and dissipation. The material properties of viscoelastic material are dependent upon time, temperature, and loading path. Hence, these characteristics have to be considered when performing structural optimization. Studies on the constitutive equations of viscoelastic material are widely carried out, and structural optimization using harmonic excitation in the frequency-domain is often reported. However, structural optimization in the time-domain is rarely performed. One of the reasons is that the cost of sensitivity analysis is quite expensive. The Equivalent Static Loads Method (ESLM) is a linear/nonlinear dynamic response structural optimization method. In this research, a practical structural optimization method to consider the characteristics of viscoelastic material is proposed using ESLM. Equivalent static loads (ESLs) are defined as the static loads that generate the same displacement field as that from dynamic analysis. In ESLM, dynamic analysis and linear static response optimization are alternatively repeated until convergence is achieved. Viscoelastic material reduces the vibration amplitude and the stored energy in a structural system. Thus, excellent damping performance is required for a part with viscoelastic material, while the proper stiffness is maintained. An appropriate design formulation is made for the design of viscoelastic material. In this research, the sum of damping ratios, the sum of weighted damping ratios, and the sum of squared displacements are considered as the objective functions. These three objective functions deal with the peak displacements of damped vibration. Three case studies are defined by optimizations of some typical automotive parts with viscoelastic material. They are a sandwich panel, a rubber bushing, and a seat cushion. The damping performances of the objective functions are compared and discussed.

Nonlinear Dynamic Response Structural Optimization of a Joined-Wing Using Equivalent Static Loads

2009 ◽  
Vol 46 (3) ◽  
pp. 821-831 ◽  
Author(s):  
Y. I. Kim ◽  
G. J. Park ◽  
R. M. Kolonay ◽  
M. Blair ◽  
R. A. Canfield
Keyword(s):  
Dynamic Response ◽  
Structural Optimization ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Response ◽  
Static Loads ◽  
Equivalent Static Loads ◽  
Joined Wing
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