Topological optimization of the plate
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Abstract
The paper provides the procedure of forward-engineering (intelligent) plate design. This technology is an exclusive modification of topological (bionic) optimization. It is based on the new energy principles and the algorithms for successive construction of geometric and/or physical-mechanical “pattern” of a structure.
The sequence of computational operations of the method in question is illustrated on example of forming plate of energetically uniform strength.
The solution is built analytically to show the nuances of the operations required. The decision of the future analytically helps to show the nuances of the necessary operations. At the same time, on the given supports, it is shown that the introduced optimization criteria determine, at the same time together, the minimum volume of constructs, and also their minimum deflections.
A fundamental element of the given approach is the use of a new criterion for the limit state, which provides an estimate of the element’s stress. In this case, the properties of the material and the type of the stress and strain state are taken into account.
The analytical solution obtained was used as a checkup test for the general computational procedure of the method in question. In this connection, the paper features the results of analytical and numerical solutions. The efficiency of the computational procedure is confirmed by the rate of its convergence and the minimal variation of geometrical construction parameters (topology) with test cases. The technological sequence of computational operations of the method in question is completed by the construction of elements (plate) with basic external and complex internal geometry, which provides a holistic set of positive power structures, such as minimum consumables in a fixed brutal state, or maximum weight in a fixed organization.
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References
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