روش بدون شبکه توابع پایه ‌نمایی با مرتبه پیوستگی دلخواه برای خمش صفحات مرکب لایه‌ای

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی عمران، دانشگاه صنعتی اصفهان

چکیده

در این مقاله یک روش بدون شبکه محلی براساس فرمول‌بندی ترفتز به منظور تحلیل رفتار خمشی ورق‌های کامپوزیت لایه­ای بدون محدودیت در آرایش لایه‌ها توسعه داده شده است. مدل‌سازی صفحات با استفاده از تئوری تغییرشکل برشی مرتبه اول (میندلین) صورت گرفته است. در روش پیشنهادی دامنه حل شامل ناحیه داخل و مرزهای دامنه به وسیله‌ دو مجموعه از شبکه نقاط گسسته­سازی می‌شود. نقاطی که حاوی مجهولات درجات آزادی هستند نقاط گره‌ای، و نقاط شبکه‌ دوم که به منظور تشکیل معادلات تعریف می‌شوند نقاط واسطه نامیده می‌شوند. متناظر با هر یک از این نقاط یک زیردامنه به نام ابر حاوی تعدادی از نقاط گره‌ای مجاور در نظر گرفته می‌شود. در این روش، جواب مسئله از مجموع دو بخش همگن و خصوصی حاصل شده و برای درون‌یابی هر کدام از یک سری متشکل از توابع پایه نمایی استفاده می‌شود. فرمول‌بندی این روش قابلیت ایجاد پیوستگی با مراتب دلخواه میان زیرناحیه‌ها بدون اضافه نمودن هرگونه درجه آزادی را دارا است، به این صورت که مقادیر درجات آزادی و یا مشتقات آن­ها تا مرتبه دلخواه در هر نقطه گره­ای توسط مقادیر متناظر از نقاط گره­ای مجاور همان ابر درونیابی می­شوند، سپس همپوشانی ابرها این پیوستگی را به کل دامنه سرایت می­دهد. برای بررسی کارایی و دقت روش، نتایج حاصل با حل دقیق مسئله در صورت وجود، و یا با سایر مراجع مقایسه می‌شوند که همگی بیانگر عملکرد بسیار خوب روش هستند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Meshless Local Exponential Basis Functions with Up-To-Desired Continuity Order for Bending of Laminated Composite Plates

نویسندگان [English]

  • Alireza Motamedi
  • Nima noormohammadi
  • Bijan Boroomand
Department of Civil Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
چکیده [English]

This paper presents a meshless local method based on Trefftz formulation for bending analysis of laminated composite plates regardless of the lamination scheme. The plates are modelled based on Mindlin’s first order shear deformation theory. In the proposed method, the solution domain is discretized by two sets of point grids, namely the nodal grid that contain the degrees of freedom (DOFs), and the intermediate point grid that have no DOFs, but are only used for imposition of the governing equations and the boundary conditions. A subdomain, named cloud, is considered corresponding to every node, which contains a definite number of its adjacent nodes. The problem solution is constituted of homogeneous and particular parts within the cloud, where exponential basis functions are used to interpolate each part. The implemented formulation is capable of extending continuity of the DOFs up to desired order of derivatives, by only interpolating the intended DOF by means of its corresponding DOFs from the nodes in its close neighborhood within the cloud in a weighted residual approach, without introducing extra DOFs. The overlap of adjacent clouds integrates the solution function over the entire domain. To investigate the applicability and accuracy of the proposed method, numerical examples will compare the extracted solutions by their exact counterparts or available data in the literature, which reflect perfect performance of the method.

کلیدواژه‌ها [English]

  • Composite plate
  • Mindlin’s theory
  • Trefftz
  • Meshless method
  • Exponential basis functions

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