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<p>To model the correct mechanical behavior of materials at lower length scales, various continuum-scale models have been proposed by introducing length scale parameters in their formulations. In this direction, current study presents a combined nonlocal strain gradient theory for the bending analysis of composite nanoplates using both third-order shear deformation theory and classical laminated plate theory. The constitutive relationships are reformulated to incorporate both nonlocal and strain gradient effects by length scale parameters. An analytical solution is presented for the modified governing equations using Navier’s approach. Parametric studies to investigate the influence of the nonlocal parameter (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>) and the strain gradient parameter (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell ^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ℓ</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>) on the bending response of laminated composite nanoplates are carried out. The results demonstrate the desired cumulative effect of stiffness softening and hardening by both these parameters for different plate characteristics. The current formulation reduces to classical continuum model in limiting cases; when the length scale values are zero, it shows good agreement with the existing literature, thus validating the robustness of the proposed model.</p>

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Nonlocal strain gradient model for bending analysis of laminated composite nanoplates using higher-order shear deformation effects

  • 期刊论文

  • 发表日期：

    2026年3月19日

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  • Aurojyoti Prusty,
  • Mingyang Zhang,
  • Weilun Wang

摘要

To model the correct mechanical behavior of materials at lower length scales, various continuum-scale models have been proposed by introducing length scale parameters in their formulations. In this direction, current study presents a combined nonlocal strain gradient theory for the bending analysis of composite nanoplates using both third-order shear deformation theory and classical laminated plate theory. The constitutive relationships are reformulated to incorporate both nonlocal and strain gradient effects by length scale parameters. An analytical solution is presented for the modified governing equations using Navier’s approach. Parametric studies to investigate the influence of the nonlocal parameter ( \(\mu \) μ ) and the strain gradient parameter ( \(\ell ^2\) ℓ 2 ) on the bending response of laminated composite nanoplates are carried out. The results demonstrate the desired cumulative effect of stiffness softening and hardening by both these parameters for different plate characteristics. The current formulation reduces to classical continuum model in limiting cases; when the length scale values are zero, it shows good agreement with the existing literature, thus validating the robustness of the proposed model.