استفاده از يك روش MLPG جديد براي مطالعه‌ي اثر زاويه گراديان مواد بر ضريب شدت تنش مود تركيبي در ورق هاي مدرج تابعي

New Mlpg Method For Studying The Effect Of Material Gradation Angle On Mixed-Mode Sif Of Fg Plates

روش بدون مش محلي پتروف ـ گالركين (MLPG) يك روش بدون مش واقعي است كه در سال هاي اخير مورد توجه بسياري از محققين قرار گرفته است. تا سال 2002 شش نوع مختلف اين روش براساس تابع آزمون انتخابي معرفي شده كه در ميان آنها از روش MLPG1 بيش از ساير روش‌ها در تحليل مسايل مهندسي كاربرد داشته است. اما در سال 2012 يك روش MLPG جامع جديد براي حل مسايل الاستواستاتيك معرفي شد. اين روش قادر به يكسان‌سازي انواع مختلف MLPG است و بالقوه نتايج چهار نوع MLPG را در درون خود دارد. در اين نوشتار براي اولين بار از روش MLPG جامع جديد براي تحليل ورق ترك‌دار مدرج تابعي استفاده شده است. ضريب شدت تنش مود اول و دوم تحت تاثير نسبت ناهمگني، طول ترك و زاويه‌ي گراديان خواص مختلف محاسبه شده و نتايج با روش مرسوم MLPG1 و حل دقيق مقايسه شده است.

Functionally graded materials (FGMs) are a good solution for sharp interface problems between two dissimilar materials. These materials contain a continuous, or discontinuous, gradient in composition, which can be designed to meet specific needs while providing the best use of composite components. To solve FGM crack problems, the use of computational methods, such as FDM, FEM and MFree, is inevitable. The meshless local Petrov-Galerkin (MLPG) method is a truly meshfree method that has become of interest to many researchers in recent years. Six different types of MLPG method were introduced on the basis of different test functions. The MLPG1 is one of the most common meshless methods used to solve different types of engineering problem. In 2012, a new unified MLPG method was also introduced to solve elastostatic problems. Using this new method, four common types of MLPG can be approached, and may unify the various kinds of MLPG. In this paper, for the first time, the new unified MLPG method is used to analyze the FGM cracked plate. The stress intensity factor of Mode I and Mode II is determined under the influence of various non-homogeneity ratios, crack lengths and material gradation angles. In this method, both the moving least square (MLS) and direct methods have been applied to estimate the shape function and to impose the essential boundary conditions. The enriched weight function method is used to simulate the displacement and stress field around the crack tip. Normalized stress intensity factors are calculated using the path independent integral, J*, which is formulated for the non-homogeneous material. The FGM edge-cracked plate is considered here and analyzed under uniform membrane and uniform fixed grip conditions with the new MLPG method, and the results compared with common MLPG1 and the exact solution. With this new method, results show higher accuracy compared to MLPG1. The present method may thus be substituted for common MLPG approaches to solve such problems.