Abstract
In its original formulation, Michell’s (Philosophical Magazine, Series 6 8(47):589–597, 1904) problem reads as follows: find the framework of least volume in which state of stress \(\varvec{\sigma }\) satisfies the conditions \(-\sigma _C \le \min \lambda _i(\varvec{\sigma })\le \max \lambda _i (\varvec{\sigma }) \le \sigma _T\) and which a given load transmits to a given segment of the boundary of the design domain; \(\lambda _i (\varvec{A})\) represents ith eigenvalue of a symmetric matrix \(\varvec{A}\). The solution to this problem depends essentially on the ratio \(\kappa =\frac{\sigma _T}{\sigma _C}\) but does not depend on other material data. Therefore, this problem belongs to the class called the plastic optimum design.
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Notes
- 1.
The non-typical notation T for the axial force is taken from Hemp (1973).
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Lewiński, T., Sokół, T., Graczykowski, C. (2019). Selected Problems of Statics. In: Michell Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-95180-5_1
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