روش هم هندسی

The isogeometric method was introduced to bridge the gap between computer-aided design (CAD) and analysis. This method offers advantages such as precise geometric modeling, suitable refinement methods, easy access to higher-order functions, and higher computational accuracy. The aim of this research is to provide an efficient method for applying the distributed loads on curved surfaces in isogeometric analysis. One of the main challenges in this method is how to apply boundary conditions on complex geometries. In curved models, some control points may not lie on the geometry, leading to ambiguity in the distribution of loads on these points. This study uses NURBS functions, which are standard non-interpolatory functions in CAD systems, to approximate the solution space and describe the geometry. Additionally, to leverage the capabilities of CAD tools, the process of importing geometries created in Rhino into isogeometric analysis using Bézier extraction is explained. The results confirm the accuracy and efficiency of the proposed method.

Unlike metals for which the fracture characterization methods have been standardized in the context of linear elastic and elastic plastic fracture mechanics theories, for polymeric materials the linear and especially nonlinear theories of viscoelastic fracture mechanics has not been completely developed due to complexities regarding the viscoelastic nature of these materials. For rubbers, even the rate independent theories based on nonlinear finite elasticity have not been widely used. In practice, most researchers make use of the same methods as applied for metals to rubbers. In this paper, the common methods of fracture characterization of rubbers based on J integral and the different challenges regarding them are reviewed. Specificly, the energy dissipation effects in regions far from the crack tip and the correction methods proposed to compensate for these effects are discussed. Performing fracture toughness tests on SENT specimens of a rubbery material based on polybutadiene, it is shown that the well-known multiple specimen method for determination of Jc has a strong sensitivity to experimental errors that exhibits itself as initial crack length dependence of Jc values and is just usefull when testing numerous specimens and removing the experimental errors. On the other hand, the locus method of dissipation correction, gives a single reliable Jc value using a fewer number of specimens and with a considerably lower sensitivity to the experimental errors. Also, using this method the specimen length dependence of Jc values reported in the literature is removed, and hence, it is possible to obtain a dimension independent Jc value.