Prof. Herbert Mang, had a visit to AMSS and gave a lecture titled “the Buckling Sphere——A Symbiosis of Mechanics and Geometry” at AMSS on 31, May, 2016.
The basis of this work is a novel symbiosis of mechanics of solids and spherical geometry to quantify and illustrate the variation of the “non-membrance” percentage of strain energy in the pre-buckling region of elastic structures. 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 energy percentage. For the limiting case of buckling from a membrance stress state this curve degenerates to a point, characterized by 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 both the “non-membrance” deformations and of the stiffness of the structure at incipient buckling. The azimuth angle is computed with the help of the so-called consistently linearized eigen-problem, which is solved by means the Finite Element Method. This eigenvalue problem is the basis for a hypothesis for the “non-membrance” 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 four examples, referring to buckling from a membrance stress state, a pure bending stress state, and a general stress state. The practical motive for this research is the intention to investigate the influence of “non-membrance” action just before buckling on the initial post-buckling behavior of elastic structures.
Prof. Herbert Mang comes from Vienna Uni. Of Technology, and he is the Academician of National Academy of Engineering.
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