报告摘要 / ABSTRACT

The motivation for this work, which is research in progress, is to link differential geometry and solid mechanics to split the strain energy of statically and proportionally loaded structures into its membrane energy part and its non-membrane complement. The structures consist of 1-dimensional members (arches, beams) and/or 2-dimensional members (shells, plates). The non-membrane part of the strain energy generally consists of the bending energy, the transverse shear energy, and the torsional energy. Frequently, the last two energies are insignificant.

It is hypothesized that the normalized non-membrane energy part is equal to the square of the radius of curvature of a curve on the curved surface of an octant of the unit sphere. This quantity is obtained from linear eigenvalue analysis, involving the tangent stiffness matrix in the context of the FEM and an initially unknown real symmetric matrix. Considering four different options of this matrix, it has turned out in the framework of a numerical investigation that the small-displacement stiffness matrix is the sought second coefficient matrix in the mathematical formulation of the aforementioned linear eigenvalue problem. However, because of membrane locking several eigenvalue analyses, with three of the four finite elements considered, failed.

Keeping in mind that eigenvectors obtained by the FEM, representing the starting point for determination of the curvature of the previously mentioned surface curve, are N-dimensional matric vectors, one of the tasks of the research is parameter reduction in order to obtain 3-dimensional physical vectors, permitting visualization of the initially mentioned surface curve.

The present research work is embedded in a research project which is financially supported by the Austrian Science Fund. The next research step is verification of the hypothesis for shells.

报告人 / ABOUT THE SPEAKER

Herbert A. Mang教授是土木工程和计算力学领域国际知名学者，曾任奥地利科学院院长，并当选20个国家或地区的院士（中、美、德、奥等），先后兼任应用数学与力学协会等十多个国际学会的执行理事或理事及50余部国际学术期刊的编委或顾问，长期担任土木工程领域顶级期刊《Engineering Structures》主编。Mang教授先后获得欧洲计算力学协会欧拉奖章、ASCE纽马克奖章等重要奖项，2004年奥地利以其姓氏“Mang”命名了一颗小行星。Mang教授致力于推动中奥科技合作与交流，于2015年当选中国工程院外籍院士，获2019年度中华人民共和国国际科学技术合作奖。