Time：May15 09:20-09:45
Title: The Buckling Sphere A Symbiosis of Mechanics and Geometry/屈曲球体：力学和几何学的一种共生
Abstract: A novel symbiosis of mechanics of solids and spherical geometry to quantify the variation of the “non-membrane” percentage of the strain energy in the prebuckling region of elastic structures is proposed. The zenith angle of an arbitrary point of a specific curve on an octant of the unit sphere, called buckling sphere, is related to this percentage. For the limiting case of a membrane stress state this curve degenerates to a point, with zero values of both spherical coordinates. For all other stress states the azimuth angle increases with the proportionally increasing load. Its magnitude at the stability limit correlates with a quantity that depends on the “non-membrane” deformations and the stiffness of the structure at incipient buckling. The azimuth angle is computed with the help of the so-called consistently linearized eigenproblem, which is solved by means of the FEM. This eigenvalue problem is the basis for a hypothesis for the “non-membrane” percentage of the strain energy. In the theoretical part of the paper, the concept of the buckling sphere is presented. Thereafter, its numerical realization is described. The subsequent numerical investigation consists of examples concerning buckling from a membrane stress state, a pure bending stress state, and a general stress state.
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