Multicriteria parametric optimization of the strength of an aluminum cylindrical shell taking into account geometric nonlinearity under thermostress loading

Abstract

Shells are thin-walled spatial structures that have the most efficient shape for transferring external forces with minimal material consumption. Thermal stress, which arises from the simultaneous action of mechanical forces and significant temperature fields or gradients, significantly complicates the behavior of shell structures.

Traditional design methods, which are based primarily on strength at fixed geometric parameters, are often insufficient. They can lead to excessive strength reserves (increased weight and cost) or, conversely, fail to ensure reliability by ignoring nonlinear interaction effects. This is why there is a need for parametric optimization—a method that allows for systematic investigation of the influence of numerous design variables (geometric, material, thermal) on the behavior of a structure and finding its optimal configurations according to a given criterion.

Parametric optimization, unlike topological or shape-forming optimization, aims to find the best values for a fixed set of parameters (thickness, radius of gyration, angle of inclination).

As part of the sensitivity analysis, the gradients of the design variables and displacements are calculated as partial derivatives of these characteristics with respect to the design variables and shell thickness. The sensitivity information serves as the basis for constructing an optimal design algorithm using the gradient descent method of the objective function.

After a numerical experiment in Fig. 1.3, the maximum Mises stresses are 240 MPa, with the shell thickness varying from 2 mm to 30 mm depending on the loading zone. The graph of objective functions shows a decrease in the weight of the aluminum cylindrical shell from 68,800 kg to 51,300 kg, which is 25.4% in percentage terms, while the Mises stress increased from 68 MPa to 240 MPa. All numerical studies were performed in an automated mode using proprietary software and the Femap with Nastran calculation complex.

This numerical method is effective for studying the optimal design of spatial thin-walled structures under thermo-mechanical loading.