Objective Submillimeter wave telescopes require reflector panel surface accuracy at the micrometer level. This precision is essential for diffraction-limited performance at wavelengths near 350 μm. Panel support structures must resolve a fundamental engineering conflict. They need high static stiffness to resist gravity-induced deformation under varying elevation angles. At the same time, they require controlled flexibility to accommodate differential thermal expansion without generating stress concentrations or warping. Traditional design approaches rely heavily on iterative finite element analysis. These methods treat the structure as a numerical black box. They offer little insight into the physical origins of parasitic displacements and rotations. Their computational cost grows rapidly with model complexity. Design cycles become prohibitively slow for large-scale systems. This work addressed these limitations by developing a physics-informed analytical framework. The goal was efficient multi-objective optimization of support geometry. The framework needed to balance static rigidity and thermal adaptability in a transparent, interpretable manner.

Methods An analytical flexibility matrix model was constructed using screw theory. The model targeted the four-point symmetric support configuration commonly used in large submillimeter telescopes. Each support leg consisted of a circular-section flexible rod. These rods acted as compliant elements with well-defined mechanical behavior. Closed-form displacement-force relationships were derived for individual rods. The same formulation extended to the integrated panel-support system. These expressions enabled direct calculation of panel-level rigid-body motions and elastic deformations from applied loads. No numerical solvers were required during evaluation. All analytical flexibility coefficients underwent rigorous validation. High-fidelity finite element models served as benchmarks. Absolute relative errors across all coefficients remained below 1.5%. A global sensitivity analysis examined entries in the flexibility and stiffness matrices. It identified specific off-diagonal terms most responsible for parasitic translations and rotations. These terms directly contributed to surface RMS error. They became the core objective functions in a multi-objective optimization problem. Design variables included the length and radius of both inner and outer support rods. These parameters control directional compliance without altering topology. The NSGA-II evolutionary algorithm generated a Pareto front of optimal solutions. The entire optimization loop operated exclusively on the analytical model. No finite element simulations were called during the process. This eliminated the primary bottleneck in conventional workflows. Preliminary experimental validation tested a full-scale aluminum panel prototype. A coordinate measuring machine recorded three-dimensional surface coordinates. Complementary photogrammetry provided dense point-cloud data. Tests covered five telescope elevation angles to simulate gravity vector changes. Thermal cycling spanned –40 °C to +40 °C in 10 °C steps. Surface repeatability and thermal drift were quantified under realistic operating conditions.

Results and Discussions The optimized support geometry achieved synergistic static and thermal performance. Under gravity loading at zenith, axial (Z-direction) RMS surface error decreased from 7.6 μm to 7.0 μm. This 8% reduction confirmed enhanced resistance to panel sag. It also reflected effective suppression of parasitic rotation about transverse axes—key contributors to low-order surface aberrations. Circumferential (Y-direction) error remained stable at 1.4 μm across all orientations. This consistency verified preserved torsional rigidity around the optical axis. Radial (X-direction) error increased modestly from 4.9 μm to 6.0 μm. This change was not a failure but a strategic trade-off. Increased radial compliance allowed the panel to expand freely during heating. The benefit became evident under thermal load. A uniform 20 °C temperature rise reduced RMS surface error from 8.8 μm to 3.7 μm—a 58% improvement. The result demonstrated successful management of thermally induced deformation. Flexibility was deliberately distributed to align with expected thermal expansion modes. Computational efficiency improved by two orders of magnitude. The analytical optimization completed in minutes. Conventional finite element-based iteration required hours for comparable resolution. Total computing time dropped to 0.33% of the baseline—a 99.67% reduction. Experimental measurements showed surface errors stabilized between 12 μm and 13 μm. Errors varied by less than 1 μm across all five orientations. Thermal hysteresis was negligible after three cycles. Measured values matched analytical predictions within combined uncertainties. These uncertainties included initial manufacturing tolerances (±5 μm) and instrument resolution (±2 μm). The agreement validated the model’s predictive capability in real-world conditions. The controlled increase in X-direction compliance exemplifies a paradigm shift. Instead of maximizing global stiffness, the design redistributes directional compliance. This enables true multi-physics co-optimization. Parasitic motions are not eliminated—they are guided along benign paths. The approach recognizes that deformation is inevitable; the goal is to make it predictable and non-degrading to optical performance.

Conclusions  The screw theory-based analytical flexibility matrix model provides a transparent, interpretable foundation for high-precision support design. It establishes direct, causal links between geometric parameters and parasitic motions. This overcomes the opacity of simulation-driven black-box methods. The resulting optimization framework successfully reconciles competing demands for static rigidity and thermal compliance. It delivers measurable performance gains under both gravitational and thermal disturbances. Computational cost drops by over 99% without sacrificing accuracy. The methodology offers a robust, scalable solution for submillimeter-wave telescope reflector panels. Its principles apply broadly to other demanding opto-mechanical systems. Examples include space telescopes, cryogenic spectrometers, and adaptive secondary mirrors. Any application requiring micron-level stability under multi-physics loads can adopt this approach. The model’s analytical nature enables rapid design exploration, sensitivity studies, and real-time compensation strategies. Future work will extend the framework to asymmetric support layouts and non-circular rod cross-sections. Integration into full-reflector co-design pipelines is underway. Coupling with active alignment systems could enable closed-loop thermal compensation. This work establishes a new design philosophy: precision through intelligent flexibility, not brute-force stiffness.