Wrinkling in graded core/shell systems using symplectic formulation
Wrinkling in graded core/shell systems using symplectic formulation
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DOI：
10.1007/s10483-023-3057-7
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发表时间：
2023-11
影响因子：
--
通讯作者：
Yaqi Guo;Guohua Nie
中科院分区：
文献类型：
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作者：
Yaqi Guo;Guohua Nie
最近通过能量法将平面分级弹性层中的皱纹描述为时变哈密顿系统。圆柱形核/壳结构在外部压力下也会经历表面不稳定性。在这项研究中，我们表明，通过将径向方向视为伪时间变量，具有径向衰减弹性特性的分级核/壳系统也可以在辛框架内描述。结合壳屈曲方程，本文通过求解一系列变系数常微分方程来解决均匀外压作用下分级核/壳结构的表面起皱问题。展示了三种代表性的梯度分布，并通过有限元模拟验证了预测的临界压力和临界波数。辛框架提供了一种有效而准确的方法来理解弯曲生物组织和工程结构的表面不稳定性和形态演化。
Wrinkles in flat graded elastic layers have been recently described as a time-varying Hamiltonian system by the energy method. Cylindrical core/shell structures can also undergo surface instabilities under the external pressure. In this study, we show that by treating the radial direction as a pseudo-time variable, the graded core/shell system with radially decaying elastic properties can also be described within the symplectic framework. In combination with the shell buckling equation, the present paper addresses the surface wrinkling of graded core/shell structures subjected to the uniform external pressure by solving a series of ordinary differential equations with varying coefficients. Three representative gradient distributions are showcased, and the predicted critical pressure and critical wave number are verified by finite element simulations. The symplectic framework provides an efficient and accurate approach to understand the surface instability and morphological evolution in curved biological tissues and engineered structures.