The stiffness and heat dissipation of thin planar structures in industrial engineering are taken as the background for this research. Plant leaves with various vein patterns, such as tobacco (Nicotiana tabacum L.) and chili (Capsicum annuum L.) leaves, are treated as the research objects. Through a combination of morphological and mechanical analysis, the distribution patterns and properties of leaf veins are mathematically characterized. A topological optimization algorithm is employed to simulate the vein growth process, thus revealing the effects of the mechanical and biological properties of different leaves on their vein morphologies. Additionally, the angles between the main and secondary veins are controlled to satisfy biological constraints. This comprehensive exploration of vein morphological formation can serve as a reference for the design of bionic thin planar structures in engineering.

以薄薄的平面结构在工业工程中的刚度和散热为研究背景。植物的叶片具有各种静脉模式，例如烟草（Nicotiana tabacum L.）和辣椒（Capsicum annuum L.）。）叶子，被视为研究对象。通过形态分析和力学分析相结合，可以对叶脉的分布模式和特性进行数学表征。拓扑优化算法用于模拟静脉生长过程，从而揭示了不同叶片的机械和生物学特性对其静脉形态的影响。另外，主静脉和次静脉之间的角度被控制以满足生物学限制。对静脉形态学形成的全面探索可以为工程中仿生薄平面结构的设计提供参考。