Nonlinear axisymmetric bending analysis of strain gradient thin circular plate

A size-dependent nonlinear bending theory for axisymmetric thin circular plate is proposed by using the principle of minimum potential energy. The formulation is based on the strain gradient theory of Zhou et al. and the von Karman geometric nonlinearity. The governing equations and boundary conditions are obtained and further reduced to that based on the couple stress theory, modified couple stress theory and even classical theory by neglecting some or all strain gradient components, respectively. Besides, the corresponding linear theory is also obtained by excluding the nonlinear terms from the present theory. The bending problems for both simply supported and fully clamped circular plate subjected to uniformly distributed load are solved by using the differential quadrature method (DQM) and iteration method. The comparison between theoretical and numerical results of linear bending deflection shows good agreement. The numerical results of nonlinear bending deflection based on these different theories reveal the size-dependency of circular plate bending rigidity. The effect of strain gradients enhances the bending rigidity of circular plate, in which rotation gradient plays a dominant role in controlling the stiffening effect of bending rigidity. When the thickness of circular plate is close to the higher-order material constant, the strain gradient effects are comparable or even dominant in comparison with the traditional bending rigidity. When the thickness of circular plate is much greater than the higher-order material constant, all strain gradient effects can be ignorable and the differences of deflections among these theories are negligible. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

A size-dependent nonlinear bending theory for axisymmetric thin circular plate is proposed based on the strain gradient theory, with governing equations and boundary conditions obtained and simplified based on different stress theories. The bending problems are solved using the differential quadrature method and iteration method, showing the enhancement of bending rigidity due to strain gradients. The numerical results reveal the size-dependency of circular plate bending rigidity and the dominant role of rotation gradient in controlling the stiffening effect.