It is common to manufacture an object by decomposing it into parts that can be assembled. This decomposition is often required by size limits of the machine, the complex structure of the shape, etc. To make it possible to easily assemble the final object, it is often desirable to design geometry that enables robust connections between the subcomponents. In this project, we study the task of dovetail-joint shape optimization for stiffness using gradient-based optimization. This optimization requires a differentiable simulator that is capable of modeling the contact between the two parts of a joint, making it possible to reason about the gradient of the stiffness with respect to shape parameters. Our simulation approach uses a penalty method that alternates between optimizing each side of the joint, using the adjoint method to compute gradients. We test our method by optimizing the joint shapes in three different joint shape spaces, and evaluate optimized joint shapes in both simulation and real-world tests. The experiments show that optimized joint shapes achieve higher stiffness, both synthetically and in real-world tests.

翻译：在制造物体时，常通过将其分解为可组装部件来实现，这种分解通常受限于机床尺寸限制、形状复杂结构等因素。为便于最终物体的组装，设计具有可靠连接特性的子部件几何形状至关重要。本课题基于梯度优化方法研究面向刚度的燕尾榫接头形状优化问题。该优化需采用可微仿真器建模接头两部件间的接触行为，从而推导刚度关于形状参数的梯度。我们的仿真方法采用罚函数法，交替优化接头两侧的几何形状，并利用伴随矩阵法计算梯度。通过在三种不同接头形状空间中优化设计案例，我们验证了该方法在仿真环境与真实场景下的有效性。实验表明，优化后的接头形状无论在合成测试还是实际应用中均能实现更高刚度。