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若干弹性力学问题解的唯一性定理 被引量:3
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作者 高梦霓 赵亚溥 《中国科学:物理学、力学、天文学》 CSCD 北大核心 2020年第8期52-85,共34页
弹性力学问题解的适定性,包括存在性、唯一性以及稳定性(对边界条件的连续依赖性).其中解的唯一性定理是求解定解问题的一个有力工具,为各种求解方法提供理论依据,解是否满足唯一性是弹性理论的一个基本问题.然而,在物理上三维弹性问题... 弹性力学问题解的适定性,包括存在性、唯一性以及稳定性(对边界条件的连续依赖性).其中解的唯一性定理是求解定解问题的一个有力工具,为各种求解方法提供理论依据,解是否满足唯一性是弹性理论的一个基本问题.然而,在物理上三维弹性问题存在非唯一解的例子广泛存在,其相应的数学模型并不能要求解的唯一性定理无条件成立.因此解的唯一性需在一定的条件下成立,如弹性张量、应变能函数和变形范围的限制条件.本文回顾了解的唯一性定理在弹性理论中的背景和发展历史,重点介绍了线性弹性理论、有限变形非线性弹性理论和具有初始应力场的弹性理论中边值问题的解的唯一性定理,给出了其中重要定理的证明方法.在此基础上,结合研究进展提出了弹性力学问题解的唯一性定理的待解决问题. 展开更多
关键词 弹性理论 边值问题 唯一性定理 本构关系 应变能函数 凸性
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Formation of wavy-ring crack in drying droplet of protein solutions 被引量:3
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作者 gao mengni HUANG XianFu ZHAO YaPu 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2018年第7期949-958,共10页
The formations of desiccation cracks and their patterns in drying droplets of protein solutions are studied experimentally. The solvent evaporation causes the dehydration self-organization phenomenon in colloidal drop... The formations of desiccation cracks and their patterns in drying droplets of protein solutions are studied experimentally. The solvent evaporation causes the dehydration self-organization phenomenon in colloidal droplets, followed by the formations of desiccation cracks. Two categories of highly ordered crack patterns, which we name "daisy" and "wavy-ring", are identified in the drying droplets. We explore the shifting of crack patterns from the "daisy" to the "wavy-ring" by varying the concentration of protein droplets. The results show that the concentration correlates with the pattern of deposition film directly, and modulates the periodicity of the crack pattern. We investigate the formations and periodicities of these two kinds of crack patterns, and obtain the scaling law of periodicity of the "wavy-ring" crack pattern. The relationship between the deposition pattern and the highly ordered crack patterns is also examined. This study will help in understanding the formation mechanisms of crack patterns in drying droplets of protein solutions and assist the future design of crack patterns in practical applications. 展开更多
关键词 蛋白质 微滴 戒指 干燥裂缝 溶剂蒸发 未来设计 试验性 频率
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