Changzheng Cheng

Diffusion-induced stress (DIS) in layered electrodes during lithium-ion battery cycling critically influences battery performance and lifetime. This study develops a computational approach integrating the boundary element method (BEM) and radial integration method (RIM) for efficient DIS calculation. The BEM offers higher computational efficiency than the finite element method by achieving accurate results with fewer elements and reduced computation time, thereby lowering computational costs in electrode design. The proposed method simplifies the electrode into a layered structure, solves the elastic equilibrium equation using BEM, and applies RIM to handle domain integrals involving the lithium-ion concentration field. Investigations demonstrate that variations in the partial molar volume of the active layer significantly affect DIS distribution and magnitude. Comparisons of mechanical responses under constant-current (CC) and constant-voltage (CV) charging reveal that initial CC charging induces less deformation and lower DIS than CV charging. Thus, a CC-to-CV charging strategy is recommended to mitigate DIS, enhancing cycle life and safety.

Purpose: The nearly singular integrals will occur when the interior points are closing to the boundary in the boundary element method. The conventional Gauss integral cannot effectively deal with the nearly singular integrals, which will lead to inaccurate numerical results for near-boundary interior points. Due to the determination of boundary unknown needing the information of interior points in the transient problem, the accurate numerical results for interior points are vital for the transient heat conduction boundary element method. Design/methodology/approach: In this paper, the dual reciprocity method is applied to transform the time-dependent domain integrals in transient heat conduction problems into pure boundary integrals by introducing the radial basis functions. The time-dependent terms are expressed in finite difference form using a set of coefficients that correspond with the radial basis functions. The nearly singular integrals are normalized on the local coordinate system. The analytical integral formulas for nearly singular integrals in boundary integral equations are derived through the Gaussian divergence theorem and integration by parts. Findings: By introducing different coefficients that match the radial basis functions, the proposed method can be applied to analyze the transient heat conduction problems with heat sources or with variable heat conductivity coefficient. Three numerical examples show that the proposed method can evaluate the transient temperature field of interior points much closer to the boundary. The proposed method eliminates the need for domain discretization, which will reduce both the difficulty of element discretization and the computational cost. Originality/value: In this paper, the dual reciprocity method is applied to transform the time-dependent domain integrals in transient heat conduction problems into pure boundary integrals by introducing the radial basis functions. The time-dependent terms are expressed in finite difference form using a set of coefficients that correspond with the radial basis functions. The nearly singular integrals are normalized on the local coordinate system. The analytical integral formulas for nearly singular integrals in boundary integral equations are derived through the Gaussian divergence theorem and integration by parts.

Purpose: There are domain integrals in the integral equations for analyzing the heat conduction with a heat source.Design/methodology/approach: In order to highlight the advantages of the boundary element method, the dual reciprocity method is introduced to transform the domain integral into the boundary integral through the special interpolation function. When the internal points near the boundary are selected as the nodes for constructing the approximating functions in the dual reciprocity method, the nearly singular integrals will occur in calculating the physical quantities of these internal points. The nearly singular integrals cannot be effectively evaluated by the Gaussian numerical integration, which will reduce the calculation accuracy of the temperature and heat flux at the internal points near the boundary. Herein, a set of analytical formulas is proposed to evaluate the nearly singular integrals in the boundary integral equations for the heat conduction problem with a heat source.Findings: Thus, the accurate temperature and heat flux at the internal points closer to the boundary can be evaluated by comparing with the conventional boundary element method. The characteristic of the “boundary only” of the boundary element method is maintained for analyzing the temperature field in the heat conduction problem with a heat source.Originality/value: The boundary-domain integral equation for the heat conduction problem with a heat source is transformed into the boundary integral equation by the dual reciprocity method. Then, the analytical algorithm is introduced to evaluate the nearly singular integral in the heat conduction boundary integral equations with a heat source. The present method retains the “boundary only” characteristic of the boundary element method and effectively evaluates the nearly singular integrals when the internal point is close to the boundary.

This study develops a novel singularity analysis method that addresses the limitations posed by piezoelectric material quantity and the variation patterns of property functions in functionally graded piezoelectric materials (FGPMs). Given that piezoelectric composite materials consist of multiple materials, the material properties of FGPMs vary with respect to angle. By introducing the asymptotic assumption that governs the physical fields close to the notch vertex into the static equilibrium equations, a comprehensive set of characteristic equations is formulated. All singularity orders and corresponding characteristic angle functions of the notch are determined by numerically solving the established characteristic equations. The effects of the notch opening angle, piezoelectric material polarization direction, and boundary conditions on the electromechanical field singularity at the notch are assessed. The judicious selection of material variation patterns can alleviate notch singularity in FGPMs.

The material redistribution abilities of traditional deterministic topology optimization are effective in addressing stress‐related design issues in thermal elastic structures. However, uncertainties are inevitable in real‐world. The structural strength of a design, achieved through deterministic topology optimization, is highly susceptible to these uncertainties, which may result in failure. This article introduces a novel method for topology optimization in stress‐constrained thermoelastic structures, taking into account the uncertainties associated with heat sources and loads. We employ the Kieisselmeier–Steinhauser function to aggregate the stress constraint when constructing the performance function. In order to improve optimization efficiency, the sequential optimization and reliability assessment method is used to decouple the double‐layer loop reliability‐based topology optimization. Initially, we derive the derivative of stress‐based performance functions with respect to heat source and load uncertainty variables, thereby facilitating the use of modified chaos control for assessing structural reliability and imposing constraints. The adjoint method and chain rule are utilized to obtain the derivative information of the performance function with respect to density variables, guiding the topology updates. We present five design examples to demonstrate the effectiveness of the presented method. Monte Carlo simulations for the optimized results are performed to show that the presented method can obtain a structure that meets reliability requirements.