Inverse design of variable-thickness curved-beam structures for nonlinear mechanical signal transformation

This study presents a novel kind of variable-thickness curved-beam-based structure (VTCB) that significantly expands the design space for lateral displacement curves under large deformations. To efficiently and accurately achieve desired lateral displacement curves, we propose a two-step inverse design framework combining Particle Swarm Optimization (PSO) and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. This method effectively navigates the high-dimensional design space, achieving optimal solutions through an initial global search followed by fine-tuning while minimizing surrogate model-induced errors. Using this approach, we realize unconventional lateral displacement curves, including multiple directional reversals, V-shaped profiles, and trigonometric function-based curves—configurations difficult to achieve with traditional methods. Furthermore, leveraging VTCB's broad performance space, we develop a customizable quasi-static mechanical signal transformer capable of various signal conversions, such as waveform transformation (e.g., converting a sine wave into a triangular wave, quasi-square wave, or pulse signal), frequency multiplication, and wave rectification by inverting or blocking specific signal components. The proposed VTCB enables advanced nonlinear displacement transformations in mechanical systems and lays the foundation for future applications in mechanical computation, programmable materials and structures, robotics, and beyond.