نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، مهندسی مکانیک، دانشگاه تربیت مدرس، تهرا ن.

2 استاد، دانشکده مهندسی مکانیک، دانشگاه تربیت مدرس، تهران.

10.22068/jstc.2021.523813.1700

چکیده

در این تحقیق به تحلیل رفتار خمشی ورق مربعی هایپرالاستیک چندلایه با شرایط مرزی گیردار، ساده و آزاد پرداخته شده است. برای استخراج معادلات حاکم بر مسئله از تانسور تغییر شکل کوشی-گرین راست استفاده شده و به دنبال آن از تابع انرژی کرنشی نئوهوکین برای توصیف رفتار غیرخطی مادی ورق استفاده شده است. برای فرمولبندی کرنش‌های غیرخطی، تئوری تغییر شکل برشی مرتبۀ اول به کار رفته و برای استخراج معادلات حاکم بر ورق هایپرالاستیک به فرم قوی، روابط اویلر-لاگرانژ به کار رفته‌اند. برای حل معادلات غیرخطی حاکم بر مسئله از روش بدون شبکه به فرم قوی بر پایۀ درونیابی نقاط شعاعی استفاده شده است. یکی از مزایای مهم این روش، اعمال شرایط مرزی غیرخطی در فرآیند حل مسئله است. از تابع پایۀ شعاعی لگاریتمی برای استخراج توابع شکل روش بدون شبکه استفاده شده و دستگاه معادلات غیرخطی حاصل از درونیابی نقاط شعاعی با استفاده از الگوریتم طول کمان بررسی شده است. نتایج حاصل از روش بدون شبکه با نتایج نرم افزار المان محدود آباکوس مقایسه شده است. نتایج این تحقیق نشان می‌دهند که روش بدون شبکه به فرم قوی بر اساس توابع پایۀ شعاعی دارای دقت بالایی در شرایط مرزی مختلف بوده به طوری که کمترین مقدار اختلاف در شرایط مرزی گیردار با 0.93 درصد اختلاف و بیشترین مقدار اختلاف در شرایط مرزی آزاد با 8.72 درصد اختلاف است.

کلیدواژه‌ها

عنوان مقاله [English]

Nonlinear bending analysis of multi-layer hyperelastic silicon-rubber plates using meshless based on radial basis functions

نویسندگان [English]

  • Shahram Hosseini 1
  • Gholamhossein Rahimi 2

1 Department of mechanical engineering, Tarbiat Modares University, Tehran, Iran.

2 Department of mechanical engineering, Tarbiat Modares University, Tehran, Iran.

چکیده [English]

In this paper, bending analysis of a hyperelastic multi-layer square plate with clamped, simply supported, and free boundary conditions are studied. The right Cauchy-Green tensor and neo-Hookean strain energy function utilized to define the plate's physical nonlinear behaviour. The nonlinear strains formulated using first-order shear deformation plate theory, and the Euler-Lagrange equations employed to derive the strong form of the governing equations. The meshless collocation method based on radial point interpolation method used to solve the nonlinear governing equations. The nonlinear boundary conditions imposed directly on the plate in meshless collocation method. The logarithm basis function utilized for defining shape functions, and the nonlinear system of equations solved using the arc-length algorithm. The results of the meshless method compared to those of ABAQUS finite element software. The results show that the meshless collocation method based on radial basis functions are efficient in nonlinear bending analysis of the multi-layer hyperelastic plate with various boundary conditions such that the less difference between meshless method and finite element method is 0.93% for clamped and the most difference is 8.72% with free boundary conditions.

کلیدواژه‌ها [English]

  • Multi-layer hyperelastic plates
  • Meshless method
  • Radial basis functions
  • neo-Hookean strain energy function
[1] Amabili, M., Balasubramanian, P., Ferrari, I. D. B. G., Garziera, R. and  Riabova, K., “Experimental and Numerical Study on Vibrations and Static Deflection of a Thin Hyperelastic Plate“ Journal of Sound and Vibration, No. September, 2016.
[2] Breslavsky, I., Amabili, M. and  Legrand, M., “Physically and Geometrically Nonlinear Vibrations of Thin Rectangular Plates“, Vol. 3, No. 2, pp. 1-2, 2012.
[3] Du, P., Dai, H. H., Wang, J. and  Wang, Q., “Analytical Study on Growth-Induced Bending Deformations of Multi-Layered Hyperelastic Plates“ International Journal of Non-Linear Mechanics, Vol. 119, pp. 103370-103370, 2020.
[4] Chen, R. M., “Some Nonlinear Dispersive Waves Arising in Compressible Hyperelastic Plates“ International Journal of Engineering Science, Vol. 44, No. 18-19, pp. 1188-1204, 2006.
[5] Li, G. Y., He, Q., Mangan, R., Xu, G., Mo, C., Luo, J., Destrade, M. and  Cao, Y., “Guided Waves in Pre-Stressed Hyperelastic Plates and Tubes: Application to the Ultrasound Elastography of Thin-Walled Soft Materials“ Journal of the Mechanics and Physics of Solids, Vol. 102, pp. 67-79, 2017.
[6] Gacem, H., Chevalier, Y., Dion, J. L., Soula, M. and  Rezgui, B., “Nonlinear Dynamic Behaviour of a Preloaded Thin Sandwich Plate Incorporating Visco-Hyperelastic Layers“ Journal of Sound and Vibration, Vol. 322, pp. 941-953, 2009.
[7] Dervaux, J., Ciarletta, P. and  Ben Amar, M., “Morphogenesis of Thin Hyperelastic Plates: A Constitutive Theory of Biological Growth in the Föppl–Von Kármán Limit“ Journal of the Mechanics and Physics of Solids, Vol. 57, No. 3, pp. 458-471, 2009.
[8] Wang, J., Song, Z. and  Dai, H. H., “On a Consistent Finite-Strain Plate Theory for Incompressible Hyperelastic Materials“ International Journal of Solids and Structures, Vol. 78-79, pp. 101-109, 2016.
[9] Tripathi, A. and  Bajaj, A. K., “Topology Optimization and Internal Resonances in Transverse Vibrations of Hyperelastic Plates“ International Journal of Solids and Structures, Vol. 81, pp. 311-328, 2016.
[10]Karp, B. and  Durban, D., “Evanescent and Propagating Waves in Prestretched Hyperelastic Plates“ International Journal of Solids and Structures, Vol. 42, pp. 1613-1647, 2005.
[11]Singh, J. and  Shukla, K. K., “Nonlinear Flexural Analysis of Laminated Composite Plates Using Rbf Based Meshless Method“ Composite Structures, Vol. 94, No. 5, pp. 1714-1720, 2012.
[12]Tu, W., Gu, Y. T. and  Wen, P. H., “Effective Shear Modulus Approach for Two Dimensional Solids and Plate Bending Problems by Meshless Point Collocation Method“ Engineering Analysis with Boundary Elements, Vol. 36, pp. 675-684, 2012.
[13]Hussein Al-Tholaia, M. M. and  Jubran Al-Gahtani, H., “Rbf-Based Meshless Method for Large Deflection of Elastic Thin Plates on Nonlinear Foundations“ Engineering Analysis with Boundary Elements, Vol. 51, pp. 146-155, 2015.
[14]Lei, Z. X., Zhang, L. W. and  Liew, K. M., “Meshless Modeling of Geometrically Nonlinear Behavior of Cnt-Reinforced Functionally Graded Composite Laminated Plates“ Applied Mathematics and Computation, Vol. 295, pp. 24-46, 2017.
[15]Jaworska, I. and  Orkisz, J., “On Nonlinear Analysis by the Multipoint Meshless Fdm“ Engineering Analysis with Boundary Elements, Vol. 92, pp. 231-243, 2018.
[16]Liu, C. S. and  Wang, F., “A Meshless Method for Solving the Nonlinear Inverse Cauchy Problem of Elliptic Type Equation in a Doubly-Connected Domain“ Computers and Mathematics with Applications, Vol. 76, pp. 1837-1852, 2018.
[17]Kumar, A. and  Bhardwaj, A., “A Local Meshless Method for Time Fractional Nonlinear Diffusion Wave Equation“ Numerical Algorithms, pp. 1311-1334, 2020.
[18]Wang, J. F., Yang, J. P., Lai, S. K. and  Zhang, W., “Stochastic Meshless Method for Nonlinear Vibration Analysis of Composite Plate Reinforced with Carbon Fibers“ Aerospace Science and Technology, Vol. 105, pp. 105919, 2020.
[19]Gholamipoor, M. and  Ghiasi, M., “Wave Propagation in Meshless Numerical Wave Tank by Using Hermite-Type Rpim“ Engineering Analysis with Boundary Elements, Vol. 121, pp. 233-242, 2020.
[20]Vaghefi, R., “Three-Dimensional Temperature-Dependent Thermo-Elastoplastic Bending Analysis of Functionally Graded Skew Plates Using a Novel Meshless Approach“ Aerospace Science and Technology, Vol. 1, pp. 105916-105916, 2020.
[21]Zheng, H., Sladek, J., Sladek, V., Wang, S. K. and  Wen, P. H., “Hybrid Meshless/Displacement Discontinuity Method for Fgm Reissner's Plate with Cracks“ Applied Mathematical Modelling, Vol. 90, pp. 1226-1244, 2021.
[22]Hosseini, S. and  Rahimi, G., “Nonlinear Bending Analysis of Hyperelastic Plates Using Fsdt and Meshless Collocation Method Based on Radial Basis Function“ International Journal of Applied Mechanics, Vol. 13, No. 01, pp. 2150007, 2021/01/01, 2021.
[23]Rodrigues, D. E. S., Belinha, J., Dinis, L. M. J. S. and  Natal Jorge, R. M., “A Meshless Study of Antisymmetric Angle-Ply Laminates Using High-Order Shear Deformation Theories“ Composite Structures, Vol. 255, pp. 112795, 2021.
[24]Palizvan, A., Mossaiby, F. and  Amoushahi, H., “Bending and Buckling Solution of Composite Viscoelastic Plate Using the Generalized Exponential Basis Function Method“, Vol. 6, pp. 190-199, 2019.
[25]Aghamohammadi, H., Abbandanak, S. N. H., Eslami-farsani, R. and  Hossein, S. M., “Effect of Various Surface Treatment Methods on the Flexural Properties of Fiber Metal Laminates“, Vol. 6, pp. 495-502, 1398.
[26]Azghan, M. A., Fallahnejad, M., Zamani, A. and  Eslami-farsani, R., “Investigation the Flexural Behavior of Fiber Metal Laminates Containing Glass and Kevlar Fibers Subjected to Thermal Cycling“, Vol. 7, pp. 981-988, 2020.
[27]Xia, P. and  Wei, K., “Shear Locking Analysis of Plate Bending by Using Meshless Local Radial Point Interpolation Method“ Applied Mechanics and Materials, Vol. 166-169, pp. 2867-2870, 2012.