International Journal for Numerical Methods in Engineering最新文献

The symplectic algorithm for Hamiltonian systems is renowned for its high accuracy and efficiency in long-term computations. However, its direct application to non-conservative problems in engineering dynamics is limited by the presence of dissipative effects and external load terms. To overcome these challenges, this paper presents a novel symplectic precise integration method based on the perturbation series approach, specifically tailored for structural dynamic response problems. By introducing a state vector, the general structural dynamic response equation is reformulated into a generalized Hamiltonian framework. Subsequently, perturbation theory is applied to transform this generalized Hamiltonian equation into a sequence of linear Hamiltonian equations, effectively converting the problem of solving non-conservative equations into one of solving multiple conservative equations. The precise integration method is then used to derive a step mapping matrix that significantly improves accuracy without substantially increasing computational cost. Numerical examples are provided to highlight the efficacy and practical applicability of the proposed method in addressing complex structural dynamic response problems.

The uncertainty in a vehicle's position and dynamic state at the end of the Mars atmospheric entry significantly influences the successful deployment of the parachute. This uncertainty is primarily driven by measurement uncertainties, including those associated with the vehicle's initial state and model parameters. These uncertainties propagate through the dynamic system, thereby contributing to the overall uncertainty in the vehicle's terminal state. Traditionally, errors in the vehicle's position and dynamic state are evaluated separately using different indicators. However, successful parachute deployment depends on both the vehicle's position and dynamic state. This paper presents a method that integrates errors in both the vehicle's position and dynamic state to quantify the uncertainty in the terminal state of Mars entry vehicles, considering various contributing factors. The method also assesses the probability of successful parachute deployment. First, a covariance matrix representing the vehicle's terminal state error is derived by propagating measurement uncertainties through the dynamic system using linear covariance analysis. A terminal state ellipsoid model is developed. Subsequently, an altitude-velocity-downrange parachute feasible deployment box is defined, considering the constraints in altitude, Mach number, dynamic pressure, and deployment position accuracy. By integrating the terminal state ellipsoid with the feasible deployment box, an integral probability model is constructed to estimate the maximum probability of successful parachute deployment within the predefined box. Numerical simulations validated the effectiveness of the terminal state ellipsoid and the integral probability model in quantifying uncertainty and demonstrating their capability to assess the vehicle's terminal position and to ensure deployment safety.

The uncertainty in a vehicle's position and dynamic state at the end of the Mars atmospheric entry significantly influences the successful deployment of the parachute. This uncertainty is primarily driven by measurement uncertainties, including those associated with the vehicle's initial state and model parameters. These uncertainties propagate through the dynamic system, thereby contributing to the overall uncertainty in the vehicle's terminal state. Traditionally, errors in the vehicle's position and dynamic state are evaluated separately using different indicators. However, successful parachute deployment depends on both the vehicle's position and dynamic state. This paper presents a method that integrates errors in both the vehicle's position and dynamic state to quantify the uncertainty in the terminal state of Mars entry vehicles, considering various contributing factors. The method also assesses the probability of successful parachute deployment. First, a covariance matrix representing the vehicle's terminal state error is derived by propagating measurement uncertainties through the dynamic system using linear covariance analysis. A terminal state ellipsoid model is developed. Subsequently, an altitude-velocity-downrange parachute feasible deployment box is defined, considering the constraints in altitude, Mach number, dynamic pressure, and deployment position accuracy. By integrating the terminal state ellipsoid with the feasible deployment box, an integral probability model is constructed to estimate the maximum probability of successful parachute deployment within the predefined box. Numerical simulations validated the effectiveness of the terminal state ellipsoid and the integral probability model in quantifying uncertainty and demonstrating their capability to assess the vehicle's terminal position and to ensure deployment safety.

Encoding velocity fields as quantum states poses a significant challenge in the development of quantum algorithms for fluid dynamics. Conventional methods, often based on direct normalization of discrete velocity data, do not intrinsically capture the structure and dynamics of vortex flows, potentially introducing artifacts that affect accuracy in modeling flow evolution. We propose a method for encoding velocity fields as quantum states of a spinor field using the spherical Clebsch representation. By applying a pointwise normalization constraint, we develop an ansatz with parameterized controlled rotation gates, optimized through a variational quantum algorithm. This approach encodes target velocity fields into spinor-based quantum states, offering a pathway to more efficient quantum simulations of fluid dynamics. Furthermore, the encoded quantum state can be mapped to the vortex-surface field, providing a useful approach for analyzing vortex dynamics and characterizing flow structures. While the calculation of the loss function encounters exponential complexity per training step, and the measurement of all qubits is inevitable, leading to high computational complexity for implementation on quantum hardware and requiring further optimization, its effectiveness has been validated across various scenarios through quantum simulation. This method enables spinor-based encoding and quantum simulation, with potential applications to diverse vector fields and complex flows, including magnetohydrodynamics and reactive flows.

The piezoelectric effect in piezoelectric materials facilitates the transformation of mechanical energy into electrical energy, with significant applications in energy generation, aerospace, biomedical engineering and other sophisticated technologies. In this study, a Multi-field coupled Multiphase hybrid finite element method (MFCMHFEM) is discovered. The multiphase composite material enhances material properties while reducing fracture and fatigue characteristics. In the multiphase material element, independent force and electric displacement fields are established. For each phase, corresponding stress and electric displacement functions are constructed to analyze the piezoelectric composite material. Based on the principle of minimum complementary energy and using the Lagrange multiplier to implement several constraints, the modified complementary energy functional of the multiphase hybrid finite element is derived. The accuracy of the proposed method is ultimately validated by comparing the computational results of the piezoelectric MFCMHFEM model with those from the ABAQUS software through several numerical examples. The model is further employed to investigate the macroscopic equivalent physical and mechanical properties of piezoelectric composites in relation to microstructural details, including the volume ratio of the inclusion to the matrix, the number of inclusions, and the orientation of polarization. This method offers an effective approach to studying the micro- and macro-electromechanical coupling of piezoelectric composites with numerous inclusions.

The piezoelectric effect in piezoelectric materials facilitates the transformation of mechanical energy into electrical energy, with significant applications in energy generation, aerospace, biomedical engineering and other sophisticated technologies. In this study, a Multi-field coupled Multiphase hybrid finite element method (MFCMHFEM) is discovered. The multiphase composite material enhances material properties while reducing fracture and fatigue characteristics. In the multiphase material element, independent force and electric displacement fields are established. For each phase, corresponding stress and electric displacement functions are constructed to analyze the piezoelectric composite material. Based on the principle of minimum complementary energy and using the Lagrange multiplier to implement several constraints, the modified complementary energy functional of the multiphase hybrid finite element is derived. The accuracy of the proposed method is ultimately validated by comparing the computational results of the piezoelectric MFCMHFEM model with those from the ABAQUS software through several numerical examples. The model is further employed to investigate the macroscopic equivalent physical and mechanical properties of piezoelectric composites in relation to microstructural details, including the volume ratio of the inclusion to the matrix, the number of inclusions, and the orientation of polarization. This method offers an effective approach to studying the micro- and macro-electromechanical coupling of piezoelectric composites with numerous inclusions.

This paper develops a family of energy-conserving time integration methods for nonlinear conservative dynamical problems. Constructed within a unified, self-starting, and single-solve integration framework, the proposed methods avoid multi-stage or sub-step procedures, leading to improved computational efficiency while maintaining robust accuracy. By using a nonlinear conservative single-degree-of-freedom system as a benchmark, the proposed framework systematically derives the conditions under which higher-order consistency in conserving the total energy can be achieved. Three implicit integrators, called IA1-L, IA1-O, and IA1-E, are designed to minimize the local truncation error in displacement, overshoot at the first time step, and total energy error at the first time step, respectively. These three schemes are unconditionally stable and controllably dissipative, and exhibit third-order consistency in total energy conservation. To further enhance the accuracy in acceleration and total energy conservation, two identically second-order accurate implicit and explicit schemes, IA2 and EA2, are constructed to achieve fourth-order consistency in conserving the total energy. A range of numerical examples, including two linear multi-degree-of-freedom problems, a two-dimensional scalar wave propagation problem, the simple pendulum with distinct initial conditions, hardening/softening elastic springs, and the swinging wire rope with large-deformation and large-rotation, are solved and compared. The results demonstrate that the proposed methods significantly outperform the existing schemes, such as TPO/G-$��\alpha �$ and EG-$��\alpha �$, especially in terms of total energy conservation. Moreover, for spatially discretized nonlinear problems, introducing moderate numerical dissipation further improves energy conservation and numerical stability. Overall, the proposed methods provide some efficient implicit and explicit procedures for simulating nonlinear dynamics with energy-conserving requirements.