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A super-generalized plane stress problem

Minzhong Wang (Dept. of Mechanics and Aerospace Engineering, College of Engineering, Peking Uni), Baixiang Xu (TU Darmst), Yang Gao (College of Science, China Agricultural University)

Prager Medal Symposium in honor of George Weng: Micromechanics, Composites and Multifunctional Materials

Tue 2:40 - 4:00

MacMillan 117

In this work a super generalized plane stress problem is proposed, in which the stress assumption is further reduced from the vanishing out-plane normal stress in the generalized plane stress problem to a harmonic out-plane normal stress. A stress general solution is derived for the super-generalized plane stress problem in case of isotropic elasticity. It is proved that the stress eld of the super-generalized plane stress problem can be decomposed into three parts: the plane stress state, the shear stress state, and the harmonic normal stress state. The rst two stress states have been defined in the Gregory decomposition, whereas the harmonic normal stress state is proposed for the rst time. It is also shown that the Filon average of the in-plane stress components of the super-generalized plane stress problem can be expressed by an Airy stress function. Finally, a necessary and sufficient condition is presented for the existence of biharmonic Airy stress function for the Filon averaged in-plane stresses, which is shown to be weaker than the assumption of the super-generalized plane stress problem.