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Geometry images parameterise a mesh with a square domain and store the information in a single chart. A one-to-one correspondence between the 2D plane and the 3D model is convenient for processing 3D models. However, the parameterised vertices are not all located at the intersection of the gridlines the existing geometry images. Thus, errors are unavoidable when a 3D mesh is reconstructed from the chart. In this paper, we propose parameterise surface onto a novel geometry image that preserves the constraint of topological neighbourhood information at integer coordinate points on a 2D grid and ensures that the shape of the reconstructed 3D mesh does not change from supplemented image data. We find a collection of edges that opens the mesh into simply connected surface with a single boundary. The point distribution with approximate blue noise spectral characteristics is computed by capacity-constrained delaunay triangulation without retriangulation. We move the vertices to the constrained mesh intersection, adjust the degenerate triangles on a regular grid, and fill the blank part by performing a local affine transformation between each triangle in the mesh and image. Unlike other geometry images, the proposed method results in no error in the reconstructed surface model when floating-point data are stored in the image. High reconstruction accuracy is achieved when the xyz positions are in a 16-bit data format in each image channel because only rounding errors exist in the topology-preserving geometry images, there are no sampling errors. This method performs one-to-one mapping between the 3D surface mesh and the points in the 2D image, while foldovers do not appear in the 2D triangular mesh, maintaining the topological structure. This also shows the potential of using a 2D image processing algorithm to process 3D models. [ABSTRACT FROM AUTHOR]

In this paper, a density-based topology optimization method using neural networks is used to design domains composed of multi-materials under combined thermo–mechanical loading. The neural network produces the topology density field by minimizing a loss function defined for the problem. Length scale control is conducted using a Fourier space projection. JAX, a high-performance automatic differentiation (AD) Python library is used to build an end-to-end differentiable neural network. The model can handle the sensitivity analysis automatically using the backpropagation process (automatic differentiation of loss function) and the need for solving adjoint equations manual sensitivity analysis is removed. The optimization problem is solved by minimizing the loss function of the network and other optimization algorithms such as the Method of Moving Asymptotes (MMA) are not required. The performance of the method is demonstrated through several examples and compared with those obtained from the popular Solid Isotropic Material with Penalization (SIMP) method. The network is able to handle high-resolution re-sampling, resulting in a more refined and smooth variation of optimal topologies. • A neural network-based topology optimization (TO) method is proposed. • The method is intended for multi-material domains under combined loading. • The NN utilizes JAX for automatic sensitivity analysis. • The loss function of the NN is minimized to solve the TO problem. • The method's effectiveness is demonstrated through examples. [ABSTRACT FROM AUTHOR]

Fail-safe robustness is an important design philosophy for critical structural systems such as airframes. The basic idea of fail-safe design is that a structure should be designed to survive normal loading conditions when local damage occurs. In the context of topology optimization, fail-safe consideration innovates the morphogenesis for structural design in addition to the parametric safety margin. Existing fail-safe topology optimization methods usually enumerate all/predefined possible damages among the design domain and optimize the worst-damage scenario. However, virtually all damages can occur and cause the structural system to stop functioning. This work proposes the Stochastic Fail-Safe Topology Optimization (S-FSTO) for computationally viable fail-safe topology optimization which considers all possible damages according to the associated severity, including the worst-damage scenario. Critical damages for density value updates are sampled through the proposed two-level sampling strategy, which allows arbitrary size and location of damages. A design domain segmentation strategy is proposed to improve the sampling efficiency. The required number of FEA runs could be reduced by multiple orders of magnitudes. The proposed S-FSTO could be conveniently equivalent to a variety of existing schemes by customizing the proposal distributions of the two-level sampling strategy. The dependence on subjective decisions for selecting local damages could be minimized. The proposed framework has been evaluated for the design of cantilever beams and airplane bearing brackets. The generated conceptual designs are significantly more robust than the deterministic ones when local damage occurs. For the design of cantilever beams, S-FSTO produced designs with similar performance as that from the original FSTO and saved 99.4% FEA runs. • A unifying and computationally viable framework for Fail-Safe design. • A two-level sampling technique considering both location and severity of damage. • An integrated parallelization scheme of U-FSTO through design domain clustering. • Innovative fail-safe designs for beams, airplane bearing brackets and bridges. [ABSTRACT FROM AUTHOR]