Study On Scale Effect Of Stress Concentration Around Holes In Thin Plates

Represented by Micro-Electro-Mechanical System, the microstructure has great application prospect due to its miniaturization, integration, mass production and other prominent advantages. However, more and more experiments have shown that structures display obvious scale effect when their length scales are at the level of micro dimension. The classical elastic theories can not explain the phenomenon. In addition, open-hole components are widely used in project fields such as mechanical, civil engineering and aerospace engineering. Stress concentration around the holes is one of the ubiquitous and crucial problems must be paid enough attention. Therefore, it is important for theoretical research and engineering application to establish new elastic theory models which can take the scale effect into consideration, and apply them to the analysis about stress concentration problem of microstructures.Based on the generalized linear elastic theory model developed by Professor Zhanfang Liu, the scale effect of the stress concentration in thin plates with holes was analyzed systematically. The principal contents in this dissertation are as follows:① The complete generalized elastic theory was developed. The essence of this model is that the elastic deformation is decomposed into translational and rotational deformation, described by strain tensor and curvature tensor respectively. Besides, the strain tensor and curvature tensor are work conjugate to symmetric stress and couple stress correspondingly. The particle is satisfied with the equations of linear and angular momentum conservation and the curvature tensor and couple stress are satisfied with a linear constitutive law. The generalized elasticity completes the geometric description of small deformation. In addition, it is able to reflect the scale effect of microstructures, so is more suitable for mechanical analysis of structures from macroscopic to microscopic.② Using penalty function method to introduce the constraints of rotation vector, the finite element control equations of the generalized elastic body are derived by the principle of virtual work and the constrained variational principle, with both the displacement and rotational angle considered as independent variables. The 4-nodes and 12-dofs quadrilateral isoparametric element corresponding to the plane problem of the generalized elastic body and the 8-node and 48-dofs hexahedral isoparametric element corresponding to the three-dimensional problem were constructed.③ The stress concentration problem of finite-width thin plates with a central circular hole subjected to the uniaxial uniformly distributed tension and simple shear respectively were researched. Stress concentration factors related to different dimensions of the thin plate were obtained. Analysis showed that stress concentration factors under different conditions display strong scale effect: the two kinds of stress concentration factors decreased to 1.822 and 1.095 respectively, is far less than the 3.052 and 2.095 calculated by the classical elastic theory.④ The scale effect of shear stress reciprocal theorem in classical elasticity was investigated. The total stress symmetry, an indicator used to measure the symmetry of the stress was introduced. The research on the scale effect of total stress symmetry corresponding to different positions and dimensions of the thin plate subjected to simple shear showed that the shear stress reciprocal theorem has sufficient accuracy for elastomer at the macro scale, however, for micro scale elastomer, the stress is no longer symmetrical, and the asymmetry of stress becomes stronger and stronger when the dimension of the plate decreases gradually. Furthermore, the total stress symmetry of thin plates under uniaxial tension and simple shear was analyzed, and the qualitative interpretation on the scale effect of stress concentration factor was given.⑤ Numerical analysis on the scale effect of stress concentration factors of thin plates with difform central elliptic holes showed that the scale effect is more obvious while the shape of the elliptic holes are sharper and the dimension is smaller.The main works and conclusions in this dissertation can provide an important reference value for the theoretical research and engineering design of micro thin plates with holes.