中国科学技术大学学报
中國科學技術大學學報
중국과학기술대학학보
Journal of University of Science and Technology of China
2015年
9期
757-762
,共6页
非欧弹性板%目标度量张量%目标高斯曲率%弯曲能%拉伸能
非歐彈性闆%目標度量張量%目標高斯麯率%彎麯能%拉伸能
비구탄성판%목표도량장량%목표고사곡솔%만곡능%랍신능
non-Euclidean plate%target metric%target Gaussian curvature%bending energy%stretching energy
不均匀温度膨胀会导致平板发生面外变形，这对应于非欧弹性板理论中板壳在目标度量张量作用下的空间变形．利用经典的弹簧网络模型模拟了一系列不同膨胀函数作用下的非欧弹性圆板变形，得到了目标高斯曲率 K正负不同的特征变形．针对 K＜0的圆盘，分析了不同厚度 t情况下波数随膨胀强度提高的演化．研究了 t恒定时圆盘在不同膨胀强度和应变梯度作用下弯曲能占总能量比例的变化，当圆盘变形后波数变化时，弯曲能比例急剧变化．同一膨胀函数作用下，得到了圆盘拉伸能和弯曲能对厚度的标度率，当 K＞0时拉伸能和弯曲能均和 t2．5相关，当 K＜0时弯曲能和 t2．5相关，拉伸能和 t4相关．
不均勻溫度膨脹會導緻平闆髮生麵外變形，這對應于非歐彈性闆理論中闆殼在目標度量張量作用下的空間變形．利用經典的彈簧網絡模型模擬瞭一繫列不同膨脹函數作用下的非歐彈性圓闆變形，得到瞭目標高斯麯率 K正負不同的特徵變形．針對 K＜0的圓盤，分析瞭不同厚度 t情況下波數隨膨脹彊度提高的縯化．研究瞭 t恆定時圓盤在不同膨脹彊度和應變梯度作用下彎麯能佔總能量比例的變化，噹圓盤變形後波數變化時，彎麯能比例急劇變化．同一膨脹函數作用下，得到瞭圓盤拉伸能和彎麯能對厚度的標度率，噹 K＞0時拉伸能和彎麯能均和 t2．5相關，噹 K＜0時彎麯能和 t2．5相關，拉伸能和 t4相關．
불균균온도팽창회도치평판발생면외변형，저대응우비구탄성판이론중판각재목표도량장량작용하적공간변형．이용경전적탄황망락모형모의료일계렬불동팽창함수작용하적비구탄성원판변형，득도료목표고사곡솔 K정부불동적특정변형．침대 K＜0적원반，분석료불동후도 t정황하파수수팽창강도제고적연화．연구료 t항정시원반재불동팽창강도화응변제도작용하만곡능점총능량비례적변화，당원반변형후파수변화시，만곡능비례급극변화．동일팽창함수작용하，득도료원반랍신능화만곡능대후도적표도솔，당 K＞0시랍신능화만곡능균화 t2．5상관，당 K＜0시만곡능화 t2．5상관，랍신능화 t4상관．
T he out‐of‐plane displacements of plates are influenced by factors such as nonuniform thermal expansion w hich corresponds the research of 3D deformation of elastomer controlled by the target metric in non‐Euclidean plates .The well‐known mass‐spring model was used to simulate the deformation of disks driven by given swelling functions corresponding positive and negative target Gaussian curvature K .The evolution of waves under negative target Gaussian curvature was analyzed with different thickness t .The impact of swelling factor and strain gradient on the ratio of bending energy to strain energy was studied with the same thicknesses .The ratio transforms rapidly when the number of waves changes for K< 0 . Scaling of stretching and bending energy about thickness was obtained while dicks were driven by the same swelling function .Stretching and bending energy both vary like t2 .5 with K > 0 ,compared with t4 of bending energy in disks with K<0 .
