This paper presents a unique solution to the problem of planar compliant mechanism design by means of geometric morphing technology and isogeometric analysis (IGA). A new transformable triangular mesh (TTM) component is developed based on geometric morphing technology, which can generate the required topology with different feature sets from a surface that has zero boundary component (interior hole) under the control of Laplace energy and mesh operations. Such flexible TTM component is helpful in overcoming the initial dependency of conventional topology optimization methods in which the layout of parameterized components often affects final optimized results. As the high-order continuity between the grids of IGA can improve calculation accuracy and numerical stability, IGA is combined with the presented TTM algorithm to establish a two-layer computational model so as to identify the optimal compliant mechanism topology within a given design domain and given displacements of input and output ports. In the upper layer of the model, the compliant limbs are characterized explicitly by triangular grids. By moving, splitting, and refining these triangular grids, the generated shape will then be projected onto the lower layer which is discretized using NURBS elements so as to calculate structural sensitivity for driving new iteration. To demonstrate the benefits provided by such method for compliant mechanism design, several numerical studies are tested, in which the geometry freely evolves along the optimization procedure, resulting in more efficient non-trivial topologies with desired kinematic behavior.

本文通过几何变形技术和等几何分析 (IGA) 为平面柔顺机构设计问题提供了独特的解决方案。基于几何变形技术开发了一种新的可变形三角形网格（TTM）组件，它可以在拉普拉斯能量和网格操作的控制下，从具有零边界组件（内孔）的表面生成所需的具有不同特征集的拓扑。这种灵活的 TTM 组件有助于克服传统拓扑优化方法的初始依赖性，其中参数化组件的布局通常会影响最终的优化结果。由于IGA网格之间的高阶连续性可以提高计算精度和数值稳定性，IGA 与所提出的 TTM 算法相结合，建立了一个两层计算模型，以便在给定的设计域和给定的输入和输出端口位移内确定最佳的顺应机制拓扑。在模型的上层，柔顺肢体由三角形网格明确表征。通过移动、分裂和细化这些三角形网格，生成的形状将被投影到使用 NURBS 元素离散化的下层，以计算驱动新迭代的结构敏感性。为了证明这种方法为柔顺机构设计提供的好处，测试了一些数值研究，其中几何形状沿着优化过程自由演化，从而产生具有所需运动学行为的更有效的非平凡拓扑。