Multicriteria parametric optimization of the strength and weight of a shell of a minimum surface on a circular contour consisting of two inclined ellipses, taking into account geometric nonlinearity under thermal and power loading
DOI:
https://doi.org/10.32347/2410-2547.2025.114.265-275Keywords:
optimization, parametric optimization, multicriteria optimization, objective function optimization, design variables, constraints, minimum surface envelopes, geometric nonlinearity, finite element methodAbstract
In the modern design of building spatial structures of the thin shell type, a new method of multicriteria parametric optimization under thermal and power loading with consideration of geometric nonlinearity has been developed. This approach to the design of the structure can be coordinated with the method of calculation for two groups of limit states. The first group of limit states includes strength and stability. The second group of limit states includes deflections and, for reinforced concrete structures, crack resistance.
External loads are taken into account in accordance with state building codes, which allow for safety factors to be taken into account with regulated safety factors for a combination of static thermal loads applied to finite elements. The calculation is performed using the finite element method in the Femap with Nastran calculation package. The optimization study is performed by connecting additional modules of our own software, which specify a pair of target Mises stress functions and the weight of the structure. The design variables are represented by the shell thickness of the minimum surface. The constraints are in the form of Mises stresses of 240 MPa, corresponding to the corresponding steel grade.
This research paper considers the object of study - a shell of minimal surface on a circular contour consisting of two inclined ellipses. This type of spatial thin shells makes it possible to use several types of optimal design simultaneously. The first type of optimal design is the optimization of the shape of the minimum surface hull, which is performed using application programs. The second type of optimal design is parametric optimization, which makes it possible to use the optimal thickness of the minimum surface shell. This approach to the design of spatial thin shells makes it possible to use minimum weight while maximizing the strength characteristics of the structure.
Numerical studies were carried out taking into account geometric nonlinearity. By taking into account the geometric nonlinearity, it was possible to take into account the actual stresses and displacements, which gave an additional optimization effect of 3% compared to the linear formulation. This approach to structural design makes it possible to use the optimization technique to calculate and design thin steel shells with minimal surfaces on real objects. This methodology has been verified by other authors.
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