| Abstrakt: |
This work presents a mechanics-informed technique to layout and design reinforcing ribs in a (quasi-)optimal manner for a thin-shell structure. The element layout follows the principal stress lines of the thin-shell continuum. The mechanics problem is solved using finite element analysis, and the result is then post-processed to determine the principal stress lines using techniques based on “streamlines.” In principal stress lines, unlike fluid mechanic streamlines, multiple directions exist at every node. This is a problem of “incomplete information,” where possible directions exist only at the nodes and the direction selection and interpolation are not trivial. Four algorithms of varying complexity and nature are proposed to address this problem, including gradient-based optimization formulations which provide an acceptable balance between computational complexity and quality of the results. The resulting principal stress lines do not necessarily coincide with the finite element nodes, which is another key novelty of this work. The (discrete) reinforcing members contribute to the overall shell stiffness by distributing (or spreading) their stiffness onto the shell, using an energy conservation approach. Finally, the laid out reinforcing members are optimally sized using a gradient-based optimizer therefore constituting a two-step procedure. The capabilities, shortcomings, and constraints of the proposed method are illustrated by means of three examples. These examples suggest that the proposed method outperforms structured and orthogonal layouts of the shell reinforcing elements. [ABSTRACT FROM AUTHOR] |
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