A simple solution method to 3D integral nonlocal elasticity: Isotropic-BEM coupled with strong form local radial point interpolation

Nonlocal theories are of growing interest as they can address problems that lead to unphysical results in the framework of classical models. In this work, a solution procedure for three-dimensional integral nonlocal elastic solid is presented. The approach is based on the partition of the displacement field into complementary and particular parts. The complementary displacement is the solution of a Navier type equation and is obtained by the boundary element method, while the particular displacement is obtained using a local radial point interpolation method. The method is illustrated by comparing the responses to some simple loadings of a solid of finite extent with the original nonlocal model of Eringen and the enhanced model of Polizzotto.     

Moisture-Driven Switching of Plasmonic Bound States in the Continuum in the Visible Region

Fast and full switching of plasmonic resonances would provide a building block for integrated electro-optically active plasmonics. To date, limited by the material properties, achieving a plasmonic resonance that can be turned fully ON and OFF in the visible region remains a formidable challenge. In this study, a nearly full optical switching based on a moisture-driven metal-hydrogel-metal (MHM) metasurface at visible frequency is experimentally realized. As a result of the bound state in the continuum (BIC)-to-quasi-BIC transition in the MHM, a sharp Fano-type quasi-BIC resonance can be switched off and back on with an ultrahigh reflectance modulation depth up to −14.6 dB within 1 s by moisture loading. Such a BIC-to-quasi-BIC transition can be well mediated by engineering the coupling between the magnetic mode and surface plasmon polariton via an active control of the gap distance between the two metallic layers. Using this concept, the MHM is demonstrated as a fast-response breathing sensor with a maximum detectable respiratory rate of up to 30 breaths per minute (bpm). These results suggest that our approach will help to realize plasmonic-based integrated active optical devices in optical sensing and modulation.     

An image denoising algorithm for mixed noise combining nonlocal means filter and sparse representation technique

Nonlocal means (NLM) filtering or sparse representation based denoising method has obtained a remarkable denoising performance. In order to integrate the advantages of two methods into a unified framework, we propose an image denoising algorithm through skillfully combining NLM and sparse representation technique to remove Gaussian noise mixed with random-valued impulse noise. In the non-Gaussian circumstance, we propose a customized blockwise NLM (CBNLM) filter to generate an initial denoised image. Based on it, we classify the different noisy pixels according to the three-sigma rule. Besides, an overcomplete dictionary is trained on the initial denoised image. Then, a complementary sparse coding technique is used to find the sparse vector for each input noisy patch over the overcomplete dictionary. Through solving a more reasonable variational denoising model, we can reconstruct the clean image. Experimental results verify that our proposed algorithm can obtain the best denoising performance, compared with some typical methods.     

An improved crack tracking algorithm with self-correction ability of the crack path and its application in a continuum damage model

In this paper, a new procedure for predicting the crack propagation and fracture behavior in quasi-brittle materials is presented based on continuum damage mechanics. Several crack tracking algorithms are widely used for failure analysis, among which the local tracking algorithm is very simple and easy to implement with low computational cost. However, in the prediction of crack growth with the traditional local tracking algorithm, it can be often seen that the sharp changes in the crack path such as U-turns can occur. An improved local tracking algorithm with self-correction ability of the crack path is proposed to overcome these difficulties of the traditional crack tracking algorithms. A continuum damage model, in addition to the present crack tracking algorithm, can greatly enhance the performance of failure prediction in quasi-brittle materials. The present approach has the advantages that it can well predict the crack propagation path and can avoid mesh size and mesh bias dependence without the embedment of discontinuities or nodal enrichment. The present model is incorporated into ANSYS by the ANSYS Parameter Design Language to simulate the initiation and propagation of the discrete crack in engineering applications. The numerical results by this model are compared with the ones by the extended finite element method and experiments, and good agreements are achieved.     

Viscoplasticity using peridynamics

Peridynamics is a continuum reformulation of the standard theory of solid mechanics. Unlike the partial differential equations of the standard theory, the basic equations of peridynamics are applicable even when cracks and other singularities appear in the deformation field. The assumptions in the original peridynamic theory resulted in severe restrictions on the types of material response that could be modeled, including a limitation on the Poisson ratio. Recent theoretical developments have shown promise for overcoming these limitations, but have not previously incorporated rate dependence and have not been demonstrated in realistic applications. In this paper, a new method for implementing a rate‐dependent plastic material within a peridynamic numerical model is proposed and demonstrated. The resulting material model implementation is fitted to rate‐dependent test data on 6061‐T6 aluminum alloy. It is shown that with this material model, the peridynamic method accurately reproduces the experimental results for Taylor impact tests over a wide range of impact velocities. The resulting model retains the advantages of the peridynamic formulation regarding discontinuities while allowing greater generality in material response than was previously possible. Copyright © 2009 John Wiley & Sons, Ltd.     

具有多约束连续体结构仿生拓扑优化方法

通过浮动参考区间法分析具有多约束连续体结构拓扑优化问题。浮动区间法是指将结构的拓扑优化过程看作是骨骼重建过程,通过引入参考应变区间,将结构中所有各点处主应变绝对值落入参考应变区间作为重建平衡状态,当结构处于重建平衡状态时获得结构的最优材料分布。为了使得优化结果满足给定的性态约束,参考应变区间在优化迭代过程中须不断变化。讨论了几种常见性态约束对结构性能的要求。给出了结构具有多约束时优化问题的算法。数值算例表明该方法可行。     

Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates

As a first endeavor, the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates is investigated using the nonlocal elasticity theory. The formulation is derived based on the first order shear deformation theory (FSDT). The solution procedure is based on the transformation of the governing equations from physical domain to computational domain and then discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. The formulation and the method of the solution are firstly validated by carrying out the comparison studies for the isotropic and orthotropic rectangular plates against existing results in literature. Then, the effects of nonlocal parameter in combination with the geometrical shape parameters, thickness-to-length ratio and the boundary conditions on the frequency parameters of the nanoplates are investigated.     

Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity

A nonlocal elastic plate model accounting for the small scale effects is developed to investigate the vibrational behavior of multi-layered graphene sheets under various boundary conditions. Based upon the constitutive equations of nonlocal elasticity, derived are the Reissner–Mindlin-type field equations which include the interaction of van der Waals forces between adjacent and non-adjacent layers and the reaction from the surrounding media. The set of coupled governing equations of motion for the multi-layered graphene sheets are then numerically solved by the generalized differential quadrature method. The present analysis provides the possibility of considering different combinations of layerwise boundary conditions in a multi-layered graphene sheet. Based on exact solution, explicit expressions for the nonlocal frequencies of a double-layered graphene sheet with all edges simply supported are also obtained. The results from the present numerical solution, where possible, are indicated to be in excellent agreement with the existing data from the literature.     

Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates

The classical and shear deformation beam and plate theories are reformulated using the nonlocal differential constitutive relations of Eringen and the von Kármán nonlinear strains. The equations of equilibrium of the nonlocal beam theories are derived, and virtual work statements in terms of the generalized displacements are presented for use with the finite element model development. The governing equilibrium equations of the classical and first-order shear deformation theories of plates with the von Kármán nonlinearity are also formulated. The theoretical development presented herein should serve to obtain the finite element results and determine the effect of the geometric nonlinearity and nonlocal constitutive relations on bending response.     

Continuum‐based design sensitivity analysis and optimization of nonlinear shell structures using meshfree method

A continuum‐based shape and configuration design sensitivity analysis (DSA) method for a finite deformation elastoplastic shell structure has been developed. Shell elastoplasticity is treated using the projection method that performs the return mapping on the subspace defined by the zero‐normal stress condition. An incrementally objective integration scheme is used in the context of finite deformation shell analysis, wherein the stress objectivity is preserved for finite rotation increments. The material derivative concept is used to develop a continuum‐based shape and configuration DSA method. Significant computational efficiency is obtained by solving the design sensitivity equation without iteration at each converged load step using the same consistent tangent stiffness matrix. Numerical implementation of the proposed shape and configuration DSA is carried out using the meshfree method. The accuracy and efficiency of the proposed method is illustrated using numerical examples. Copyright © 2006 John Wiley & Sons, Ltd.