استفاده از نيروهاي وارد بر وصله هاي تحليل ايزوژيومتريك جهت محاسبه تنش بهبود يافته و برآورد توزيع خطا

Stress Recovery and Error Estimation by Using Forces Induced on Patches of Isogeometric Analysis

در اين مقاله، يك روش جديد جهت محاسبه ميدان تنش تحليل ايزوژيومتريك بيان مي شود. در اين روش با بكار گيري نيروهاي وارد بر هر وصله از تحليل ايزوژيومتريك، سطح مربوط به هر مولفه تنش با استفاده از توابع شكل نربز هم مرتبه با توابع مورد استفاده در تخمين تابع جابجايي، تقريب زده مي شود. اين سطح تنش جديد نسبت به تنش به دست آمده از تحليل ايزوژيومتريك داراي دقت بيشتري است، لذا مي توان از آن جهت برآورد خطاي تحليل ايزوژيومتريك نيز استفاده نمود. اين برآورد كننده خطا در دسته روش هاي مبتني بر بازيافت تنش قرار مي گيرد و نشان داده خواهد شد كه كارايي بهتري نسبت به روش بازيافت تنش بر مبناي نقاط فوق همگرا در تحليل ايزوژيومتريك خواهد داشت. جهت بررسي صحت اين روش به مدلسازي و تحليل سه مسيله الاستيسيته داراي حل تحليلي و مقايسه نتايج به دست آمده از اين روش با روش مبتني بر نقاط فوق همگرا و حل دقيق پرداخته شده است. نتايج به دست آمده از تمامي مثال ها نشان دهنده كارايي مناسب اين روش مي باشد و بر اين اساس مي توان از اين روش نيز به عنوان يك روش ساده و موثر ديگر جهت بهبود تنش و برآورد خطا در روش ايزوژيومتريك نام برد. In this paper, a new method is introduced for calculation of stress field in the isogeometric analysis (IGA) method. In this technique, by considering the forces induced on the patches of IGA, the surface denoting the variations of each component of the stress tensor is approximated by the same order of NURBS’ shape functions that are used for approximation of the displacements. This new surface is more accurate compared to the stress surfaces obtained from isogeometric analysis, thereby, can be usedas error estimation of the IGA. It is shown that this method, which falls in the category of stress recovery methods, is superior to the stress recovery based on the superconvergent points in the IGA. To verify the performance of the method, three examples are taken into consideration and their solutions with this approach, as well as the method based on superconvergent points which are compared with their exact solutions. The obtained results in these examples indicate the effectiveness of the proposed method and therefore can be considered as a simple and efficient method for error estimation and stress recovery.

In this paper, a new method is introduced for calculation of stress field in the isogeometric analysis (IGA) method. In this technique, by considering the forces induced on the patches of IGA, the surface denoting the variations of each component of the stress tensor is approximated by the same order of NURBS’ shape functions that are used for approximation of the displacements. This new surface is more accurate compared to the stress surfaces obtained from isogeometric analysis, thereby, can be usedas error estimation of the IGA. It is shown that this method, which falls in the category of stress recovery methods, is superior to the stress recovery based on the superconvergent points in the IGA. To verify the performance of the method, three examples are taken into consideration and their solutions with this approach, as well as the method based on superconvergent points which are compared with their exact solutions. The obtained results in these examples indicate the effectiveness of the proposed method and therefore can be considered as a simple and efficient method for error estimation and stress recovery