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C. Thai-HoangN. Nguyen-Thanh H. Nguyen-Xuan T. Rabczuk 《Applied mathematics and computation》2011,217(17):7324-7348
This paper presents an alternative alpha finite element method using triangular meshes (AαFEM) for static, free vibration and buckling analyses of laminated composite plates. In the AαFEM, an assumed strain field is carefully constructed by combining compatible strains and additional strains with an adjustable parameter α which can produce an effectively softer stiffness formulation compared to the linear triangular element. The stiffness matrices are obtained based on the strain smoothing technique over the smoothing domains and the constant strains on triangular sub-domains associated with the nodes of the elements. The discrete shear gap (DSG) method is incorporated into the AαFEM to eliminate transverse shear locking and an improved triangular element termed as AαDSG3 is proposed. Several numerical examples are then given to demonstrate the effectiveness of the AαDSG3. 相似文献
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Yilun Liu 《Journal of the mechanics and physics of solids》2011,59(8):1613-1622
Graphene nanostrips with single or few layers can be used as bending resonators with extremely high sensitivity to environmental changes. In this paper we report molecular dynamics (MD) simulation results on the fundamental and secondary resonant frequencies f of cantilever graphene nanostrips with different layer number n and different nanostrip length L. The results deviate significantly from the prediction of not only the Euler-Bernoulli beam theory (f∝nL−2), but also the Timoshenko's model. Since graphene nanostrips have extremely high intralayer Young's modulus and ultralow interlayer shear modulus, we propose a multibeam shear model (MBSM) that neglects the intralayer stretch but accounts for the interlayer shear. The MBSM prediction of the fundamental and secondary resonant frequencies f can be well expressed in the form f−fmono∝[(n-1)/n]bL−2(1−b), where fmono denotes the corresponding resonant frequency as the layer number is 1, with b=0.61 and 0.77 for the fundamental and secondary resonant modes. Without any additional parameters fitting, the prediction from MBSM agrees excellently with the MD simulation results. The model is thus of importance for designing multilayer graphene nanostrips based applications, such as resonators, sensors and actuators, where interlayer shear has apparent impacts on the mechanical deformation, vibration and energy dissipation processes therein. 相似文献
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提出了以圆筒扭转力学模型为基础, 预测周期性多孔材料等效剪切模量及其研究尺寸效
应的一种简单有效计算方法. 以方形孔和圆形孔两种典型多孔材料为例进行了数值计算求解;
同时, 建立了几何参数随体胞尺寸缩放因子$n$的解析关系, 证明了两种构型的周期性多孔材
料的等效剪切模量均随尺寸缩放因子$n$的增大而减小. 当$n \to \infty
$时, 即体胞尺寸相对整体结构无限小时, 多孔材料的等效剪切模量趋近收敛于一个恒定值;
当体胞的材料体分比增大时, 多孔材料等效剪切模量也随之增大. 此外, 依据周
期性多孔材料的结构对称特性, 使用体胞子结构有限元计算模型进行等效剪切模量及其尺寸
效应的预测, 极大地提高了计算效率. 相似文献
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The velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional second grade fluid, between two infinite coaxial circular cylinders, are determined by applying the Laplace and finite Hankel transforms. Initially the fluid is at rest, and at time t = 0+, the inner cylinder suddenly begins to translate along the common axis with constant acceleration. The solutions that have been obtained are presented in terms of generalized G functions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for ordinary second grade and Newtonian fluids are obtained as limiting cases of the general solutions. Finally, some characteristics of the motion, as well as the influences of the material and fractional parameters on the fluid motion and a comparison between models, are underlined by graphical illustrations. 相似文献