Multicriteria parametric optimization of the stability of the minimum surface shell on a trapezoidal contour taking into account geometric nonlinearity under thermo-stress loading

Abstract

The approach to optimal design may vary depending on the types of optimization used. In this task, there is shape optimization (morphological optimization) and parametric optimization of the minimum surface shell. The selection of materials for studying the parametric optimization of minimum surface shells may not be limited to steel; other metals may also be used. The main thing is that the materials must be isotropic, i.e., have the same calculated resistance in all directions.

Verification of optimization calculation results is performed in accordance with Ukrainian building codes. After completing the optimization calculation, it is possible to superimpose the results on the thickness of the minimum surface shell on a trapezoidal contour in the Femap with Nastran calculation complex, and then perform all strength checks (calculation of statics, stability, displacement, etc.). When all verification calculations have been performed, the design engineer independently adjusts the thickness of the minimum surface shell using the initial data from the optimization calculation and designs the final thickness of the spatial structure.

Research into multi-criteria parametric optimization of stability and weight, taking into account geometric nonlinearity, is carried out using the Femap with Nastran software package. This is achieved through iterative loading and proprietary software. Finite elements: 912 plates. Nodes: 975. Connection to the ground disc – rigid clamping. Material: C275 steel.

The change in stresses according to Mises occurred from the initial 99.9 MPa to 151.1 MPa, shown in Fig. 1.12, which does not exceed the ultimate strength of steel, which is 240 MPa. The initial thickness was 60 mm, after studying multi-criteria parametric optimization, it ranges from 10 mm to 68 mm, as shown in Fig. 1.13, depending on the load zone.

Fig. 1.14 shows a graph of the objective functions of the stability coefficient λ and the weight of the minimum surface shell on a trapezoidal contour. The weight of the minimum surface shell decreased by 21.55% from the initial value. The stability loss coefficient decreased by 2.46 times, which is a fairly effective result.