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تحلیل غیرخطی هندسی المان های مستوی ابرکشسان 4 گره یی با روش لاگرانژ
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نویسنده
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ارزانی حامد ,خوش باور راد الهام
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منبع
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مهندسي عمران شريف - 1398 - دوره : 35-2 - شماره : 1/1 - صفحه:3 -12
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چکیده
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در نوشتار حاضر، فرمول‌بندی عددی کاملی برای تحلیل غیرخطی سازه‌های مستوی با مصالح ابرکشسان ارائه و مسائل المان محدود با استفاده از فرمول‌بندی لاگرانژ کامل تحلیل شده است. فرمول‌بندی ارائه‌شده برای کرنش‌های بزرگ و مواد غیرخطی ابرکشسان قابل استفاده است. همچنین فرمول‌بندی مذکور برای تحلیل مدل‌های المان محدود چهارضلعی توسعه داده شده است که نسبت به المان‌های 4 گره‌یی ایزوپارامتریک کمتر به مش‌بندی اعوجاجی حساس است و فاقد مشکل قفل‌شدگی برشی ایجادشده از طریق مش‌بندی نامنظم هندسی است. به‌منظور گسترش مزایای روش مختصات ناحیه‌ی چهارضلعی (qacm) در کاربردهای غیرخطی، از فرمول‌بندی لاگرانژی کامل المان (hy4q) استفاده شده است. دو مثال عددی ارائه‌شده و تاثیر المان hy4q در سادگی، کارایی و رفتار مناسب روش، برای تحلیل‌های غیرخطی مصالح ابرکشسان به طور قابل ملاحظه‌یی مشهود است.
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کلیدواژه
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تحلیل غیرخطی سازه، غیرخطی هندسی، المان مستوی4 گره‌یی، لاگرانژ کامل، ابرکشسان
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آدرس
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دانشگاه تربیت دبیر شهید رجایی, دانشکده مهندسی عمران, ایران, دانشگاه تربیت دبیر شهید رجایی, دانشکده مهندسی عمران, ایران
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پست الکترونیکی
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ekhoshbavarrad@gmail.com
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LAGRANGE METHOD FOR NONLINEAR SOLUTION OF HYPER ELASTIC MATERIAL BY ISOPARAMETERIC ELEMENT
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Authors
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Arzani H.
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Abstract
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In this article complete numerical formulation for nonlinear analysis of planar structures made of hyper elastic materials with application in civil engineering is presented. Structural problems can be solved by finite element method using complete lagrange formulation.The presented formulation is for large strain problems and is applicable for a wide range of hyper elastic nonlinear materials. Generally in nonlinear finite element analysis large deformation and disordered mesh (distorted) is seen. As using disordered elements, isoparametric elements would have low precision. Hyper elastic materials like rubber are one of the most effective materials in engineering application.The high axial strength and large deformation capacity of these materials make them suitable for many applications. Theory of hyper elastic materials is proposed by references [13,14].These theories explain hyper elasticity behavior in complicated formulations. Therefore we are interested in studying planar hyper elastic elements with large deformation like rubber, leather etc.Eventually planar nonlinear elements formulation with hyper elastic behavior is presented for structures having large deformations and complete lagrange formulation is used to analyze the structure. This formulation has been developed to analyze quadrilateral finite element models, which comparing to isoparametric 4node elements is less sensitive to distorted meshing and doesn't have shear locking problem generated by geometrically distorted meshing.In order to deploy 2QACM benefits in nonlinear applications, complete lagrange formulation 3Q4HY is used, numerical examples in geometric nonlinear problems have shown presented formulation's ability to prevent loss of precision in highly distorted meshing for 4node hyper elastic elements. To show effectiveness of presented elements two numerical examples are presented. Q4HY elements efficiency in nonlinear analysis of planar elements made of hyper elastic materials is significantly obvious.The program is written in matlab environment for nonlinear analysis of hyper elastic problems. Two formulations are proposed and results have been compared with references results. Examples of rubber like problems have shown these formulations ability to analyze large strain structures.Numerical examples express four node element has less sensitivity to distortion in meshing in nonlinear analysis and can be used with good precision when element is diagonal, while calculated responses using 4 node isoparametric element may be inappropriate.4 noded elements effect on developing a simple, applicable and valid nonlinear geometric analysis is significantly observed. Furthermore, a complete lagrangian formulation with a particular formulation by applying integration techniques to effectively establish stiffness matrix is presented. According to presented examples, the investigated elements have great potential in solving Hyper elastic problems.
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Keywords
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