PPubMed3 Sep 2014Cited 24×

Shape Optimization of Rubber Bushing Using Differential Evolution Algorithm

Necmettin Kaya

Abstract

The objective of this study is to design rubber bushing at desired level of stiffness characteristics in order to achieve the ride quality of the vehicle. A differential evolution algorithm based approach is developed to optimize the rubber bushing through integrating a finite element code running in batch mode to compute the objective function values for each generation. Two case studies were given to illustrate the application of proposed approach. Optimum shape parameters of 2D bushing model were determined by shape optimization using differential evolution algorithm.

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A differential evolution algorithm combined with finite‑element analysis optimizes 2D rubber bushing shape to meet target stiffness curves in two case studies.

What’s new

i.Optimized rubber bushing parameters to achieve desired stiffness levels
ii.Developed and validated a Pascal‑based differential evolution optimization software using two benchmark test functions
iii.Performed rubber material experiments to obtain hyperelastic model coefficients

How they did it

A differential evolution (DE) algorithm was implemented in Pascal and linked to Abaqus finite‑element simulations run in batch mode. Shape parameters (R1, R2, θ) were varied, and the chi‑square between simulated and target stiffness curves served as the objective function. Python scripts automated model regeneration, simulation, and objective evaluation for each DE generation.

What they found

Case Study 1 optimum parameters: R1 = 50, R2 = 12, θ = 27 (stiffness curve closely matches target)
Case Study 2 optimum parameters: R1 = 44, R2 = 5.5, θ = 29 (stiffness curve closely matches target)
Test function 1 (Rosenbrock) converged to x1 = 1, x2 = 1 at generation 40

Caveats

✕DE algorithm is slower than other evolutionary algorithms, especially for noisy problems
✕The optimization was demonstrated only on two 2D case studies, limiting assessment of broader applicability

in plain words

The researchers used a computer‑based trial‑and‑error method called differential evolution to automatically change the shape of a rubber part. They linked this method to a simulation program that predicts how stiff the part will be, and kept tweaking the shape until the simulated stiffness matched what they wanted. This lets them design the part without building physical prototypes.

why it matters

The method provides a systematic, simulation‑driven way to design rubber components, reducing trial‑and‑error cycles and speeding up vehicle suspension development. It can be extended to other rubber parts, lowering development costs across the automotive industry.

Follow the thread

rubber bushing shape optimization differential evolution finite element analysis hyperelastic material vehicle ride quality

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