Lightweight design of an electric bus body structure with analytical target cascading

Abstract

Lightweight designs of new-energy vehicles can reduce energy consumption, thereby improving driving mileage. In this study, a lightweight design of a newly developed multi-material electric bus body structure is examined in combination with analytical target cascading (ATC). By proposing an ATC-based two-level optimization strategy, the original lightweight design problem is decomposed into the system level and three subsystem levels. The system-level optimization model is related to mass minimization with all the structural modal frequency constraints, while each subsystem-level optimization model is related to the sub-structural performance objective with sub-structure mass constraints. To enhance the interaction between two-level systems, each subsystem-level objective is reformulated as a penalty-based function coordinated with the system-level objective. To guarantee the accuracy of the model-based analysis, a finite element model is validated through experimental modal test. A sequential quadratic programming algorithm is used to address the defined optimization problem for effective convergence. Compared with the initial design, the total mass is reduced by 49 kg, and the torsional stiffness is increased by 17.5%. In addition, the obtained design is also validated through strength analysis.

Key words： electric vehicle; body in white (BIW); lightweight; analytical target cascading (ATC)

Nomenclature

a_1,a_2,a_3	Scaled material properties of the side structure, roof structure, and chassis structure, respectively
A	Scaled material properties vector
c	Consistency index
d_{\mathrm{c}}^{\mathrm{L}},d_{\mathrm{c}}^{\mathrm{U}}	Maximum displacements of the chassis structure, where “L” and “U” indicate that the performance is evaluated in the subsystem level and the system level, respectively
E_i,E_{\text{o}} (i = 1,2,3)	Scaled Young’s modulus of each sub-structure and the base Young’s modulus, respectively
f_{ij}	Local objective function in ATC
f_{\mathrm{r},\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}^{\mathrm{L}},f_{\mathrm{r},\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}^{\mathrm{U}}	First-order torsional frequencies of the roof structure, where “L” and “U” indicate that the performance is evaluated in the subsystem level and the system level, respectively
f_{\mathrm{s},\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{d}}^{\mathrm{L}},f_{\mathrm{s},\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{d}}^{\mathrm{U}}	First-order bending frequencies of the side structure, where “L” and “U” indicate that the performance is evaluated in the subsystem level and the system level, respectively
f_{\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}	First-order torsional frequency of the entire structure
F_{\mathrm{s}\mathrm{y}\mathrm{s}},F_{\mathrm{s}\mathrm{u}\mathrm{b},i}	Entire structural performance and sub-structural performance, respectively
g_{ij},g	Inequality constraint
h_{ij},h	Equality constraint
M,M_{\mathrm{s}\mathrm{u}\mathrm{b},i}	Mass of the entire structure and the sub-structure, respectively
M_{\mathrm{c}},M_{\mathrm{r}},M_{\mathrm{s}}	Mass of the chassis structure, roof structure, and side structure, respectively
P_{ij}	Subsystem-level problem in ATC
r_{ij}	Response fed back to the superior level in ATC
t_{ij}	Local objective assigned from the superior level in ATC
\mathit{v}	Lagrangian multiplier vector
\mathit{w}	Quadratic punishment weight vector
{\mathit{X}}_{\mathrm{c}},{\mathit{X}}_{\mathrm{r}},{\mathit{X}}_{\mathrm{s}}	Local design variable vector of the chassis structure, roof structure, and side structure, respectively
{\mathit{X}}_{ij}	Local design variable vector in ATC
{\mathit{X}}_{\mathrm{s}\mathrm{y}\mathrm{s}}	Global design variable vector of the entire electric bus body structure
X1‒X9	Thicknesses of specific section bars in the side structure
X10‒X20	Thicknesses of specific section bars in the roof structure
X21‒X33	Thicknesses of specific section bars in the chassis structure
β	Relaxation factor
ε	Convergence threshold
{\rho }_i,{\rho }_{\mathrm{o}} (i = 1,2,3)	Scaled density of each sub-structure and the base density, respectively
\varphi \left(\mathit{c}\right)	Penalty-based coordinated function

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 51805032).

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