No abstract

The aim of this study is to investigate the effects of horizon selection on the elastic behaviour of plate type structures in the micropolar peridynamic theory. Plates with various lengths and widths have been investi-gated using micropolar peridynamic model for different horizon selections. The mathematical model of plates has been provided applying the micropolar peridynamic theory and solution of this model has been obtained by finite element methods. The displacement fields have been computed for the different horizons and dimension ratios of plates. To compute the displacement field a program code has been developed by using the software package MATHEMATICA. The results obtained have been compared with the analytical solution of the classical elasticity theory and with the solution of displacement based finite element methods. For displacement based finite element method solution the software package ANSYS has been used. Ac-cording to results it has been observed that the displacement fields of the plates are strongly affected by ho-rizon selection. Therefore a question raises that which horizon length should be used with the problem in hand or is there any method to find the appropriate/best horizon length

No abstract

No abstract

The aim of this study is to investigate the capability of the micropolar peridynamic theory to analyze elastic behavior of plates with various length and width. Since the quantities such as stress and strain are related to displacement field, only the displacement fields of these structures are computed using the micropolar peridynamic model while Poisson’s ratios are kept constant. The results are compared both to the analytical solution of the classical elasticity theory and to the solution of displacement based finite element methods. The software package ANSYS is used for FEM results. To compute the displacement field, a programming code is developed using MATHEMATICA. In the peridynamic theory the constitutive model contains only central forces and can be applied only to the materials having 1/4 Poisson’s ratio. It is the biggest shortcoming of the peridynamic theory. To overcome strict Poisson’s ratio limitation of the peridynamic theory, the micropolar peridynamic theory is proposed. The micropolar peridynamic model allows peridynamic moments, in addition to peridynamic central forces, to interact with the particles inside the material horizon. The introduction of the moments to the theory allows us to deal with the materials having Poisson’s ratio different from 1/4. This modification can be seen as the generalization of the peridynamic theory. Furthermore, the micropolar peridynamic theory can be easily implemented using the finite element methods. This provides easy application of the boundary conditions to the physical model in hand. In this work, by applying the micropolar peridynamic theory, we observed that the displacement fields of the plates are strongly affected by dimensional ratio of the plates. However, it is naturally expected that the micropolar and classical theories should give the same results, at least to a certain extend. This strong dependability on the dimensions of the structure can be a significant shortcoming of the micropolar peridynamic theory.