Technical overview of the equivalent static loads method for non-linear static response structural optimization

2010 ◽  
Vol 43 (3) ◽  
pp. 319-337 ◽  
Author(s):  
Gyung-Jin Park
Keyword(s):  
Structural Optimization ◽  
Static Response ◽  
Static Loads ◽  
Equivalent Static Loads ◽  
Non Linear ◽  
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.

Structural optimization of an automobile roof structure using equivalent static loads

2008 ◽  
Vol 222 (11) ◽  
pp. 1985-1995 ◽  
Author(s):  
S-B Jeong ◽  
S-I Yi ◽  
C-D Kan ◽  
V Nagabhushana ◽  
G-J Park
Keyword(s):  
Structural Optimization ◽  
Linear Response ◽  
Safety Regulation ◽  
National Highway Traffic Safety ◽  
Static Loads ◽  
Linear Dynamic ◽  
Equivalent Static Loads ◽  
Roof Structure ◽  
Non Linear ◽  
Response Optimization

In a vehicle rollover accident, the strength of the roof structure is an important factor of security in order to reduce the death and injury rates. The National Highway Traffic Safety Administration proposed strength requirements of the roof structure on roof crush resistance in the Federal Motor Vehicle Safety Standard (FMVSS) 216. Recently, there have been many structural optimization studies that design the structure of a vehicle to satisfy this safety regulation. Most previous studies used approximation methods such as the response surface method (RSM) as a crash problem has high non-linearity and difficulty in sensitivity calculation. However, the solution from the RSM may not be accurate and has a limit on the number of design variables. In this research, non-linear dynamic (transient) response optimization using equivalent static loads (ESLs) is proposed to design the structure of a vehicle to satisfy the safety regulation. ESLs for linear response analysis are made to generate the same displacement field as that from non-linear dynamic loads at each time step of non-linear dynamic analysis. A dynamic load is transformed to a set of ESLs. The static loads are used as the multiple loading conditions for linear response optimization, which are not costly in the linear response optimization process. Size optimization using ESLs is performed to reduce the structural mass while the FMVSS 216 regulation is satisfied. The optimum results using ESLs are compared with those from the RSM. As a result, the proposed method is very efficient and derives good solutions. Non-linear analysis is performed using the commercial code LS-DYNA. NASTRAN is used in calculating the ESL and linear response optimization. LS-OPT is utilized for structural optimization using the RSM.

Topology Optimization for Structures With Nonlinear Behavior Using the Equivalent Static Loads Method

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Hyun-Ah Lee ◽  
Gyung-Jin Park
Keyword(s):  
Topology Optimization ◽  
Nonlinear Behavior ◽  
Nonlinear Static Analysis ◽  
Static Response ◽  
Static Loads ◽  
Equivalent Static Loads ◽  
Equivalent Static Loads Method ◽  
Response Optimization ◽  
Nonlinear Static ◽  
Element Density

Many structures in the real world show nonlinear responses. The nonlinearity may be due to some reasons, such as nonlinear material (material nonlinearity), large deformation of the structures (geometric nonlinearity), or contact between the parts (contact nonlinearity). Conventional optimization algorithms considering the nonlinearities are fairly difficult and expensive because many nonlinear analyses are required. It is quite difficult to perform topology optimization considering nonlinear static behavior because of the many design variables. In the current element density based topology optimization considering nonlinear behavior, low-density finite elements cause serious numerical problems due to excessive mesh distortion. Updating the material of the finite elements based on the density is considerably complicated because of the relationship between the element density and structural material. The equivalent static loads method for nonlinear static response structural optimization (ESLSO) has been proposed for size and shape optimization. The equivalent static loads (ESLs) are defined as the linear static load sets which generate the same displacement field from nonlinear static analysis. In this research, a new algorithm is proposed for topology optimization considering all kinds of nonlinearities by modifying the existing ESLSO. The new ESLSO can overcome the difficulties which may occur in topology optimization with nonlinear static behavior. A nonlinear static response optimization problem is converted to cyclic use of linear static response optimization with ESLs. Therefore, the new ESLSO can generate results of nonlinear static response topology optimization by using well established nonlinear static analysis and linear static response topology optimization methods. Four structural examples are demonstrated using the finite element method. Different kinds of nonlinearities are involved in each example.

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