Nissan?s new hierarchical technique combines topology optimisation and shape optimisation to create innovative and light body structures with the optimal topology and smooth boundaries.
Numerical optimisation techniques are now widely used in the development process of new vehicles as a result of the rapid progress achieved by Computer Aided Engineering (CAE) in recent decades.
Sizing optimisation, such as optimisation of panel thicknesses of a vehicle body structure, is mainly applied. However, it is done only after the structural topology and the detailed shape are defined in the initial phase of the design process. It is evident that optimisation of topology and shape of a structure are highly efficient in the initial phase of the design process in terms of performance and weight aspects since changing topology or shape has a greater impact than changing panel thicknesses.
Some optimisation methods based on topology optimisation have been proposed. One such method is first-order analysis (FOA). It is applied to the grand structure consisting of beams in the admissible design domain. Another method is also based on topology optimisation using voxel elements to discretize the admissible design domain. This method helps to find the critical load paths in the design domain. However, it is very difficult to transform the resultant optimal structure made of beams or voxels into an actual shape.
Recently, shape optimisation based on the traction method has been developed. The method can generate the optimal boundary shape of a structure. Shape optimisation and topology optimisation have complementary aspects. Topology optimisation can generate a structure with a varying number of holes in the design domain although it cannot represent the smooth boundary of a structure. On the other hand, shape optimisation can maintain as smooth a boundary as that of the initial structure, though it cannot generate holes in the design domain during the shape optimisation process.
We propose a new hierarchical optimisation technique that combines topology optimisation and shape optimisation to create innovative and light body structures with the optimal topology and smooth boundaries. The results obtained can be directly applied to design drawings in the initial phase of the design process.
Topology optimisation developed by Prof. Bendsoe and Prof. Kikuchi in 1988, can solve the optimal material layout problem in the given design domain. The design domain is discretized by finite elements, and material properties such as elasticities in each element are forced to those of the base material or void through the iterative calculations. The resultant structure consisted of elements with properties of the base material gives the optimal material layout. However, it has usually jugged boundaries represented by the external shape of elements. This is not suitable for the consecutive design process.
In shape optimisation, the optimal external shape of a structure is calculated. Several methods have been proposed in the past such as super curve method and basis vector method. However, it often leads to the corrugated surface during the iterative calculations and causes numerical instabilities. Shape optimisation based on the traction method, proposed by Prof. Azegami in 1994, can help maintain as smooth a boundary as that of the initial structure in the course of iterative shape updations.
This is one of the outstanding characteristics of the method arising from the use of the elastic displacements due to the traction force proportional to the shape sensitivities to update the external shape. The resultant shape of the structure has a smooth surface and this can be applied to the following design process. However, it cannot create a new topology such as holes inside the design domain in the course of the optimisation calculations.
The proposed method is applied to optimise the front structure of a vehicle. In this example, a part of the vehicle is subjected to optimisation. Weight in the design domain is minimised under constraints that the stiffness for each static load is equal to or greater than the stiffness of the original structure and that the eigenvalue for the specified mode is equal to or greater than that of the original structure. The detailed procedures and points of view are described below.
The admissible design domain is set to the entire frontal domain except the engine and tires. The domain is discretized by voxel solid elements and is combined with the rest of the body structure as illustrated in figure 2(a). Topology optimisation is applied to the design domain under a certain set of constraints. The rest of the vehicle is fixed during the course of the optimisation process. Only static stiffness corresponding to external loads is taken into account in this hierarchy.
There are two reasons for performing the calculation in this way. One reason is the computation time. The degrees of freedom of a voxel model are likely to be much larger than those of the thin shell model. It is time consuming to calculate eigenvalues or other criteria. The other reason is that the design domain is not modelled with thin shell elements but with solid elements. This makes it impossible to compare performance between the resultant and the original structure.
The front part of a vehicle has to meet many requirements with regard to crashworthiness, stiffness and vibration. In this example, six requirements are taken into consideration through substitution into equivalent static stiffness. These include static stiffness for the fore-aft gravity load to estimate crashworthiness in full-overlap frontal crash, and static stiffness for the vertical load at an engine mounting point to estimate the vibration level produced by an engine vibratory force.
The weighted sum of the static stiffness for each load is taken as the objective function. The maximisation problem is solved by topology optimisation under the constraint of a volume fraction in the design domain. The optimal topology is shown in figure 2(b) though it has an extremely complicated material distribution.
In the second hierarchy, the thin shell structure is first created by extracting the external surface of the optimal topology. The thin shell structure shown in figure 2(c) is stepwise and not smooth; however, it can be applied as an initial structure for the second hierarchy because shape optimisation can relax it.
The thickness of the thin shell elements is set to a constant for the entire surface of the design domain. The magnitude and the direction of external loads are exactly the same as those in the first hierarchy. The weight in the design domain is regarded as the objective function, and the minimisation problem is then solved under given constraints.
We take into account as constraints the static stiffness for each load, and eigenvalues of the lateral bending mode, the vertical bending mode and the torsion mode so that corresponding values should be equal to or greater than those of the original structure. The eigen values are additionally included in the second hierarchy to account for dynamic performance.
Figure 2(d) shows the optimal shape of the thin shell structure. When we observe the resultant shape from a practical point of view, we see that smooth surfaces are obtained. The result can be applied directly to design drawings in the initial phase of the development process.
However, the optimal structure is clearly lacking several parts that would have to be present to support functional devices such as a radiator or a battery. This is due to the fact that the corresponding criteria were not taken into account here. The necessary optimisation criteria for estimating the corresponding requirements have to be provided to the optimiser to obtain a more practical result.
A new hierarchical optimisation technique to design vehicle body structure in the initial phase of development process was proposed and validated through an application to the design of a part of a vehicle body. Optimal topology can be found from the admissible design domain by topology optimisation in the first hierarchy, and optimal smooth shape of the vehicle body can be subsequently created by the traction method in the second hierarchy. The obtained result could be applied directly to design drawings, however, it should be addressed that all the necessary criteria have to be accounted to create more practical structures.
