Tornabene Francesco, Fantuzzi Nicholas, Bacciocchi Michele
DICAM-Department, School of Engineering and Architecture, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy.
Materials (Basel). 2017 Jul 17;10(7):811. doi: 10.3390/ma10070811.
A mathematical scheme is proposed here to model a damaged mechanical configuration for laminated and sandwich structures. In particular, two kinds of functions defined in the reference domain of plates and shells are introduced to weaken their mechanical properties in terms of engineering constants: a two-dimensional Gaussian function and an ellipse shaped function. By varying the geometric parameters of these distributions, several damaged configurations are analyzed and investigated through a set of parametric studies. The effect of a progressive damage is studied in terms of displacement profiles and through-the-thickness variations of stress, strain, and displacement components. To this end, a posteriori recovery procedure based on the three-dimensional equilibrium equations for shell structures in orthogonal curvilinear coordinates is introduced. The theoretical framework for the two-dimensional shell model is based on a unified formulation able to study and compare several Higher-order Shear Deformation Theories (HSDTs), including Murakami's function for the so-called zig-zag effect. Thus, various higher-order models are used and compared also to investigate the differences which can arise from the choice of the order of the kinematic expansion. Their ability to deal with several damaged configurations is analyzed as well. The paper can be placed also in the field of numerical analysis, since the solution to the static problem at issue is achieved by means of the Generalized Differential Quadrature (GDQ) method, whose accuracy and stability are proven by a set of convergence analyses and by the comparison with the results obtained through a commercial finite element software.
本文提出了一种数学方案，用于对层合结构和夹层结构的受损力学构型进行建模。具体而言，引入了在板壳参考域中定义的两种函数，以根据工程常数削弱其力学性能：二维高斯函数和椭圆函数。通过改变这些分布的几何参数，通过一组参数研究分析和研究了几种受损构型。从位移剖面以及应力、应变和位移分量的厚度变化方面研究了渐进损伤的影响。为此，引入了基于正交曲线坐标下壳结构三维平衡方程的后验恢复过程。二维壳模型的理论框架基于一种统一的公式，能够研究和比较几种高阶剪切变形理论（HSDT），包括用于所谓锯齿效应的村上函数。因此，还使用和比较了各种高阶模型，以研究运动学展开阶次选择可能产生的差异。还分析了它们处理几种受损构型的能力。本文也可归入数值分析领域，因为所讨论的静态问题的解是通过广义微分求积（GDQ）方法获得的，该方法的准确性和稳定性通过一组收敛分析以及与通过商业有限元软件获得的结果进行比较得到了证明。
