arXiv subjects

Yixiong Feng

Publications and source records attributed to Yixiong Feng.

3 recordsLinked to original sources

arXiv2026

Checkerboard Shells: A Position-Only Thin-Shell Discretization with Scale-Compatible Completion

Checkerboard edge-midpoint geometry provides an exact planar Varignon parallelogram for every spatial quadrilateral, allowing a local tangent frame and normal to be recovered directly from nodal positions even when the raw quadrilateral is warped. Building on this property, we develop a position-only thin-shell discretization with no independent director, rotation, or strain variables. The connected edge-midpoint surface is taken as the physical midsurface: the first fundamental form is evaluated on planar B faces, while a W-centered second fundamental form is constructed from variations of neighboring B-face normals, so membrane and bending share the same geometric carrier. A variational-kernel analysis shows that smooth second-order consistency does not eliminate lattice-scale blind modes. After quotienting out the raw checkerboard gauge, the B metric has one physical membrane blind direction and the symmetric W curvature has two curvature blind directions. We introduce a quotient-minimal membrane compatibility coordinate $X_M$ and an objective reference-relative curvature coordinate $X_W^{rel}$, placed consistently in the $O(t)$ membrane and $O(t^3)$ bending sectors. The formulation admits an explicit midpoint quotient, complete flat blind-mode classification, rigid-motion objectivity, reference-state consistency, and an $O(h^2)$ near-isometry approximation result for aligned generalized cylinders. Numerical tests show second-order curvature convergence, targeted removal of the membrane defect, and a sub-percent, refinement-decaying influence of $X_W^{rel}$. Linear and nonlinear shell benchmarks further demonstrate flat bending, curved-shell membrane-bending coupling, thickness sensitivity, large rotation, nonlinear pinching, and localized ovalization within a single position-only framework.

math.NA↗

arXiv2026

Inspire or Predict? Exploring New Paradigms in Assisting Classical Planners with Large Language Models

Addressing large-scale planning problems has become one of the central challenges in the planning community, deriving from the state-space explosion caused by growing objects and actions. Recently, researchers have explored the effectiveness of leveraging Large Language Models (LLMs) to generate helpful actions and states to prune the search space. However, prior works have largely overlooked integrating LLMs with domain-specific knowledge to ensure valid plans. In this paper, we propose a novel LLM-assisted planner integrated with problem decomposition, which first decomposes large planning problems into multiple simpler sub-tasks with dependency construction and conflict detection. Then we explore two novel paradigms to utilize LLMs, i.e., LLM4Inspire and LLM4Predict, to assist problem decomposition, where LLM4Inspire provides heuristic guidance according to general knowledge and LLM4Predict employs domain-specific knowledge to infer intermediate conditions. We empirically validate the effectiveness of our planner across multiple domains, demonstrating the ability of search space partition when solving large-scale planning problems. The experimental results show that LLMs effectively locate feasible solutions when pruning the search space, where infusing domain-specific knowledge into LLMs, i.e., LLM4Predict, holds particular promise compared with LLM4Inspire, which offers general knowledge within LLMs.

cs.AI↗

arXiv2023

Self-morphing of elastic bilayers induced by mismatch strain: deformation simulation and bio-inspired design

The process of self-morphing in curved surfaces found in nature, such as with the growth of flowers and leaves, has generated interest in the study of self-morphing bilayers, which has been used in many soft robots or switchers. However, previous research has primarily focused on materials or bilayer fabrication technologies. The self-morphing mechanism and process have been rarely investigated, despite their importance. This study proposed a new deformation simulation method for self-morphing bilayers based on a checkerboard-based discrete differential geometry approach. This new method achieved higher efficiency than traditional finite element methods while still maintaining accuracy. It was also effective in handling complex finite strain situations. Finally, the simulation model was used to design three self-morphing bilayers inspired by folding flowers, spiral grass, and conical seashells. These designs further prove the effectiveness of the proposed method. The results of this study propose a good method for predicting deformation and designing self-morphing bilayers and provide a useful viewpoint for using geometrical methods to solve mechanical problems.

math.NA↗