Computer Methods in Applied Mechanics and Engineering最新文献

In this study, a revised formulation based on the uniform strain method (Flanagan and Belytschko, 1981) and the scaled boundary finite element method (SBFEM) — a numerical method with arbitrarily shaped polyhedral elements — is introduced for three-dimensional elastoplastic analysis. The proposed formulation uses the average strain of each polyhedral element. By employing the octree decomposition algorithm, high-resolution images and complex STL-format geometries are automatically converted to conforming and balanced octree meshes. Furthermore, the formulation is combined with the 144 unique octree cell patterns (Zhang et al., 2021) to streamline the workflow and improve the computational efficiency. The rotating, mirroring, and scaling operations on the octree cell patterns are derived for elastoplastic analysis. Moreover, the present approach is implemented in ABAQUS as a UELMAT user element to utilize the built-in material library. The accuracy, convergence rate, and computational efficiency of the formulation are investigated using four verification examples covering octree- and arbitrary-shaped scaled boundary finite elements. The results show that the proposed formulation does not suffer from volumetric-locking, and it has achieved a 4x speed up in comparison with existing method. It is also shown that its speed is comparable to the built-in elements in the ABAQUS. Lastly, an image-based compression analysis of a steel sample and a contact analysis on a human mouth structure are performed to illustrate the automatic workflow and the improvement in the computational speed.

We propose Physics-Aware Neural Implicit Solvers (PANIS), a novel, data-driven framework for learning surrogates for parametrized Partial Differential Equations (PDEs). It consists of a probabilistic, learning objective in which weighted residuals are used to probe the PDE and provide a source of virtual data i.e. the actual PDE never needs to be solved. This is combined with a physics-aware implicit solver that consists of a much coarser, discretized version of the original PDE, which provides the requisite information bottleneck for high-dimensional problems and enables generalization in out-of-distribution settings (e.g. different boundary conditions). We demonstrate its capability in the context of random heterogeneous materials where the input parameters represent the material microstructure. We extend the framework to multiscale problems and show that a surrogate can be learned for the effective (homogenized) solution without ever solving the reference problem. We further demonstrate how the proposed framework can accommodate and generalize several existing learning objectives and architectures while yielding probabilistic surrogates that can quantify predictive uncertainty.

A variational formulation of the non-smooth contact dynamics method is proposed to address the dynamic response of historical masonry structures modeled as systems of 3D rigid blocks and subjected to ground excitation. Upon assuming a unilateral-frictional contact law between the blocks, the equations of motions are formulated in a time-discrete impulse theorem format in the unknown block velocities and contact impulses. The variational structure of the problem to be solved at each time step is proven. On that basis, the numerical method requires at each time step to perform a collision detection that identifies antagonist contact points based on the given structural configuration, to solve a second-order conic programming problem that outputs block velocities and contact impulses, and to update the structural configuration for the solution to advance in time. As a merit of the formulation, large-scale problems can be robustly and efficiently addressed thanks to the convex setting of the time-step optimization problem. Numerical results are presented to test the computational performances of the proposed approach. Benchmark problems provide numerical evidence that the formulation is consistent with event-driven solutions based on the classical Housner impact model. The dynamic response, failure domains, and fragility functions of real-size masonry structures are then explored under ground impulse or earthquake excitation. The obtained results prove the reliability of the present computational method for the dynamic analysis and seismic assessment of historical masonry constructions of engineering interest.

Time-variant reliability-based robust design optimization (TRBRDO) has achieved certain progress recently for its ability to ensure both robustness of design and feasibility of time-variant probabilistic constraints. However, the existing TRBRDO methods have not specifically addressed the dynamic uncertainty of material degradation, and there is lack of a universal and efficient approach for this class of time-variant robust design problems. For this reason, this paper proposes three solution strategies, namely the reliability index based double-loop method, performance measure based double-loop method, and sequential single-loop method. In these approaches, the minimum reliability of each time-variant probabilistic constraint is considered by obtaining the extremum in a series system. With use of the first-order reliability analysis technique, two different single-loop multivariate optimization models are established to obtain the minimum reliabilities and minimum performance measures through sequential quadratic programming algorithm, respectively. Following this, two different double-loop models and a sequential single-loop model are developed. Furthermore, an augmented step length adjustment technique is proposed for inverse reliability analysis, which is integrated into the performance moment integration and percentile difference method to derive the robustness indicators for the design objective. Finally, three illustrative numerical examples and one engineering problem are provided to demonstrate the effectiveness of the proposed solution strategies for reliable and robust design optimization with high computational efficiency.

Coronary Artery Disease (CAD) is one of the most common forms of heart disease, caused by a buildup of atherosclerotic plaque in the coronary arteries. When this buildup is extensive, it can result in obstructions in the lumen of the blood vessels (known as stenosis) that lead to insufficient delivery of essential molecules like oxygen to the heart. Fractional Flow Reserve (FFR), defined as the ratio of pressures distal and proximal to the stenosis, is the physiologic gold standard for assessing the severity of CAD in the cardiac catheterization laboratory and relies upon the placement of an invasive coronary wire. Despite its strong diagnostic value, invasive FFR assessment is underutilized due to its cost, time-consuming nature, technique-dependent variability, and the small potential of increased risk to the patient. In this study, an attention-based multi-fidelity machine learning model (AttMulFid) is proposed for efficient and accurate virtual FFR (vFFR) assessment, including uncertainty quantification, without the use of an invasive coronary wire. Within AttMulFid, an autoencoder is used to select geometric features from the coronary arteries, with additional attention to the stenosis region. A convolutional neural network (feature fusion U-Net) combines multi-fidelity data, geometric features, and boundary conditions to produce accurate estimates of vFFR. We present results that demonstrate the good performance of AttMulFid against CFD FFR data, as well as in vivo, invasive FFR assessment from patients. Our results also show that the selected geometric features learned by the autoencoder can accurately represent the entire geometry, with greater attention on key features such as stenosis. AttMulFid thus presents itself as a feasible approach for non-invasive, rapid, and accurate vFFR assessment.

We present a framework for parallel isogeometric boundary element analysis (BEA) of elastic solids on CUDA. To deal with traction discontinuities, we propose a BEA model that supports multiple nodes and semi-discontinuous elements. The multiplicity of a node is defined by the number of regions containing any element influenced by the node. A region is a group of connected elements delimited by a closed crease curve. The default shape function of an element is determined by a linear operator applied to a set of basis functions. A BEA model is supposed to be generated from a watertight boundary representation of a solid. In this paper, we employ bicubic analysis-suitable T-splines. In this case, the shape of an element is defined by its Bézier extraction operator applied to the tensor product of Bernstein polynomials of degree 3. We describe the data structures of the BEA model and the main algorithms of the analysis pipeline on CUDA. In particular, we describe two strategies for parallel assembling of the linear system of equations. We also introduce a novel approach for inside integration based on the subdivision of the singular region in triangles with constant aspect ratio. In the T-splines context, we extend the Bézier extraction to handle unstructured T-meshes with crease edges. Moreover, we propose a scheme for embedding the influence of linked tangency handles on the shape of an element directly into the Bézier extraction operator. Such an embedding enables the removal of the corresponding nodes from the BEA model and the application of an alternative collocation method we discuss in the paper. We present several experiments to evaluate the accuracy and efficiency of the proposed framework. The results demonstrate that the GPU can be advantageously employed for parallelizing T-spline-based isogeometric analysis using boundary elements, achieving a speedup of up to 29x compared to the sequential code on a current laptop. We make the BEA code available in a prototype in MATLAB with a graphical interface that allows users to apply boundary conditions and visualize analysis results on the boundary.

This research proposes a novel method for designing fracture-resistant structures. By analyzing the relationship between tensile strain energy and phase field brittle fracture, it has been found that minimizing tensile strain energy can delay fracture and enhance resistance. Capitalizing on this insight, a new topology optimization method is proposed. This method focuses on minimizing tensile strain energy to suppress the well-documented tension-dominated fracture behavior observed in phase field brittle fracture analysis. In contrast to traditional topology optimization methods based on von Mises stress, this method generates more robust structures under tension. Furthermore, the method can incorporate stress constraints to mitigate the potential for stress concentrations arising from geometric discontinuities. Numerical results demonstrate the effectiveness of the proposed method. Using phase-field modeling, the mechanical fracture properties of the optimized structures, including peak load, failure displacement, and absorbed elastic energy before fracture, are quantified. Furthermore, experimental tests are also conducted. Both numerical simulations and experimental results are consistently show that structures designed with minimized tensile strain energy exhibit superior fracture toughness. Furthermore, the method offers significant computational efficiency compared to conventional approaches due to its reliance solely on linear elasticity analysis within the optimization process.

Aligning lattice infills with the principal stress directions in loaded objects is crucial for improving stiffness. However, this principle only works for a single loading condition, where the stress field in 2D is described by two orthogonal principal stress directions. In this paper, we introduce a novel approach for designing and optimizing triangular lattice structures to accommodate multiple loading conditions, i.e., multiple stress fields need to be considered. Our method comprises two main steps: homogenization-based topology optimization and geometry-based de-homogenization. To ensure geometric regularity of the triangular lattices, we propose a simplified version of the general rank-3 laminate and parameterize the design domain using equilateral triangles with unique edge thickness. During optimization, edge thicknesses and orientations are adjusted based on the homogenized properties of the lattice. Our numerical findings demonstrate that this simplification introduces only a slight decrease in stiffness of less than 5% compared to using the general rank-3 laminate, and results in lattice structures with compelling geometric regularity. For geometry-based de-homogenization, we adopt a field-aligned triangulation approach to generate a globally consistent triangle mesh in which each triangle is oriented according to the optimized orientation field. Our approach for handling multiple loading conditions, akin to de-homogenization techniques for single loading conditions, yields highly detailed, optimized and spatially varying lattice structures. The method is computationally efficient, as simulations and optimizations are conducted at a low-resolution discretization of the design domain. Furthermore, since our approach is geometry-based, obtained structures are encoded into a compact geometric format that facilitates downstream operations such as editing and fabrication.

This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative information essential for the calculation of mechanical stresses and the computational minimisation of discretised energies. For materials, whose microstructure can be well approximated in terms of laminates and where each laminate stage achieves energetic optimality with respect to the current stage, the approximate envelope coincides with the rank-one convex envelope. Although the proposed method provides only an upper bound for the rank-one convex hull, a careful examination of the resulting constraints shows a decent applicability in mechanical problems. Various aspects of the algorithm are discussed, including the restoration of rotational invariance, microstructure reconstruction, comparisons with other semi-convexification algorithms, and mesh independency. Overall, this paper demonstrates the efficiency of the algorithm for both, well-established mathematical benchmark problems as well as nonconvex isotropic finite-strain continuum damage models in two and three dimensions. Thereby, for the first time, a feasible concurrent numerical relaxation is established for an incremental, dissipative large-strain model with relevant applications in engineering problems.

The superior stiffness-to-weight and strength-to-weight mechanical advantages of sandwich structures can be fully exploited through concurrent design of entire topology, infill configuration and density, where the high-performance yet complicated structure can be fabricated through additive manufacturing. However, the emerging design challenges are concurrent design updating related to sandwich topology, infill configuration and density, which is a design problem with continuous and discrete variables mathematically. In this paper, a concurrent topology optimization is proposed for sandwich structures with multi-configuration and variable-diameter lattice infill. Three design variable fields are employed to describe the fundamental topology considering sandwich structural topology, infill configuration and density simultaneously. Corresponding material interpolation model is developed by combining DSP-based shell-infill description and multi-response latent-variable surrogate model based effective material property calculation. Two-stage design model is formulated as a rough design model considering all design variables followed by a refined design model with only infill density variables, which is developed to strictly satisfy the material allowance constraint due to the mapping between discrete infill configuration variables and continuous latent configuration variables. Corresponding sensitivities of compliance and constraint with respect to the structural topology, infill configuration and density variables are derived, and the method of moving asymptotes (MMA) is employed to solve the design model efficiently. Several numerical examples are presented to systematically demonstrate the effectiveness of the proposed approach.