首页|超重力下立方晶格结构等效柔度的解析解

超重力下立方晶格结构等效柔度的解析解

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为全面理解生物体和航空航天器件在超重力环境下的力学行为，我们探讨了超重力对立方点阵结构等效柔度的影响。利用其周期性空间分布特性，胞元法被采用以推导出点阵结构的均质化应力应变关系，从而得到相应的等效柔度。等效柔度可方便地退化到不考虑超重力影响的情况。此外，数值模拟被执行以验证推导结果，发现超重力确实影响点阵结构的力学性能。我们引入一个无量纲的超重力因子，该因子量化了超重力大小相对于基材杨氏模量的影响。研究结果显示，超重力因子二次影响垂直柔度并线性影响平行柔度。同时，垂直剪切柔度保持不变，而平行剪切柔度则呈现反比例变化趋势。另外，点阵结构转变为超重力方向的功能梯度材料，从而也带来了尺度效应。
Analytical solutions for equivalent elastic compliance of cubic lattice structures subjected to hypergravity conditions
In order to comprehensively understand the mechanical behavior of biological entities and aerospace applications subjected to hypergravity environments,we delve into the impact of hypergravity on the equivalent compliance of cubic lattice structures.Capitalizing on the periodic spatial distribution,we employ a unit cell methodology to deduce the homogenized stress-strain relationship for the lattice structures,subsequently obtaining the associated equivalent compliance.The equivalent compliance can be conveniently reduced to instances without hypergravity influence.Furthermore,numerical simulations are executed to validate the derivations and to illustrate that hypergravity indeed affects the mechanical properties of lattice structures.We in-troduce a non-dimensional hypergravity factor,which quantifies the impact of hypergravity magnitude relative to the Young's modulus of the base material.Our findings reveal that the hypergravity factor influences perpendicular compliance quadratically and parallel compliance linearly.Simultaneously,the perpendicular shear compliance remains unaffected,whereas the parallel shear compliance experiences an inverse effect.Additionally,the lattice structure transforms into a gradient material oriented in the hypergravity direction,consequently generating a scale effect.

HypergravityCubic lattice structuresEquivalent complianceUnit cell approach

王磊、杜洋坤、王冠楠、吕朝锋

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College of Civil Engineering and Architecture,Zhejiang University,Hangzhou 310058,China

School of Mathematics and Statistics,University of Glasgow,Glasgow G12 8QQ,UK

Faculty of Mechanical Engineering and Mechanics,Ningbo University Ningbo 315211,China

Key Lab of Soft Machines and Smart Devices of Zhejiang Province,Zhejiang University,Hangzhou 310027,China

Soft Matter Research Center,Zhejiang University,Hangzhou 310027,China

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Hypergravity Cubic lattice structures Equivalent compliance Unit cell approach

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaZhejiang Provincial Natural Science Foundation of China

119252065198810112272340LD21A020002

2024

10.1007/s10409-023-23200-x

力学学报(英文版)

力学学报(英文版)

CSTPCD
影响因子：0.363
ISSN：0567-7718
年,卷(期)：2024.40(6)