The calculation of the probability distribution of performance functions is a core issue in uncertainty quantification and reliability design, and the recently proposed equivalent expectation method (EEM) is an effective way to solve this problem. This paper proposes an improved EEM. Putting forward an empirical calculation formula for the standard deviation coefficient of auxiliary random variablesand obtaining a more accurate probability distribution of the auxiliary function. Meanwhile, aiming at the accuracy issue in calculating the probability distribution of theperformance function is proposed, the calculation formula for the PDF of the performance function is derived using only one auxiliary function. In the process of calculating the PDF, proposing an exact theoretical transformation of probability distribution from auxiliary functions to performance functions is proposed, resulting in a more accurate PDF of the performance function. Finally, the effectiveness and accuracy of the method are verified through three numerical examples. The results indicate that this method is suitable for computing the probability distribution of high-dimensional nonlinear or implicit performance functions.

Small cross-sections of boundary elements easily induce the “internal tension” phenomenon of steel plate shear walls, making it difficult to fully utilize the seismic performance of buckling-restrained steel plate shear walls. The design of cross-sections of boundary elements is related to their internal force requirements, and analyzing the internal force requirements of boundary columns is meaningful. Based on the proposed buckling-restrained steel plate shear wall with multi-concrete panels (MBRSPSW), the analytical expressions for the internal force of the boundary column of the MBRSPSW were theoretically derived in this paper. Combined with the experimental research on the buckling-restrained steel plate shear wall horizontally assembled multi-concrete panels (H-MBRSPSW), its numerical model was established and verified. The internal force distributions of the boundary column obtained from numerical analysis and analytical calculation were further compared. The research results indicate that the inner steel plates in the MBRSPSW are divided into constrained regions and unconstrained regions. The axial force, shear force, and bending moment distributions of the boundary column from the analytical calculation results agree with those from the numerical analysis results, and the internal force calculation expressions of the boundary column are correct. The research results can provide a reference for the design of this category of steel plate shear walls.

A simple numerical implementation method is proposed for the Chaboche-type viscoplastic constitutive model coupled with Lemaitre anisotropic damage theory. Using the decoupled algorithm, the damage tensor is updated based on the forward difference format at the beginning of each incremental step. The damage tensor is considered as a constant in the discretization process of the constitutive equations. Based on the hypothesis of strain equivalence, the formulations containing only partial tensors are constructed in the effective deviatoric stress space, and the radial return process is simplified to solve a nonlinear scalar equation concerning the accumulated plastic strain increment. The numerical implementation method and the derivation of consistent tangent operator are provided based on the Voigt notation scheme. The comparison between the experimental data and the simulation results of isotropic scalar damage model under uniaxial and multiaxial stress states validates the effectiveness and high computational efficiency of this method. Numerical results under different time step sizes also indicate the good accuracy and stability.

Piezoelectric materials have advantages such as rapid actuation, ease of preparation, and low energy consumption. Using piezoelectric materials for vibration control can improve structural performance. Studies have shown that the distribution of piezoelectric materials can significantly impact control effectiveness. Many researchers use topology optimization techniques to optimize the layout of piezoelectric materials or control voltages. In the topology optimization of piezoelectric intelligent structures, introducing various control coefficients as design variables can achieve a larger design space and further enhance control efficiency. This paper studies the optimal distribution of control coefficients for piezoelectric layers under harmonic excitation based on the Discrete Material Optimization (DMO) method. Using a negative velocity feedback control strategy for active control, dynamic compliance is selected as the objective function to effectively measure the structural vibration level. The design variables are the negative velocity feedback control coefficients for each pair of piezoelectric sensors and actuators. Sensitivity analysis is conducted using the adjoint variable method. Finally, two numerical examples are provided to verify the correctness of the proposed method.

Using fractional derivatives to modify the Zener standard rheological solid model and considering the instantaneous rheological effect of the soil around the pile, a vertical coupled vibration model of the pile-soil system is constructed. The frequency-domain analytical solution of the system dynamic control equation is derived using Laplace transform and potential function decomposition methods. The time domain response under instantaneous excitation at the pile top is obtained through numerical Laplace inversion. Then, numerical examples are used to analyze the frequency domain characteristics of displacement and dynamic stiffness, and dynamic damping of end-bearing pile vertical vibration in a rheological clay layer, as well as the wave response under instantaneous excitation at the pile top. Research has found that the rheological effect of soil reduces the amplitude of pile top displacement and dynamic stiffness and the rheological effect of soil causes a decrease in the amplitude of the pile top response and a weakening of the reflected wave signal under instantaneous excitation.

Proppant transport in fractures is essentially a dense granular flow in a slot-shaped space. Applying the two-fluid method in numerical simulations of a field-scale particle flow is promising, but existing solid stress models cannot accurately describe the process of proppant accumulation. In this paper, the morphological change of a proppant pack under flow erosion was analyzed experimentally, and the important influence of cohesion on the change of the pack state was pointed out. Then, combined with the simulated results of a proppant transport and the results of a suspension apparent viscosity test, the influence of the particle radial distribution function on the solid kinetic pressure and the change trend of total solid pressure were analyzed, and the change rate of the solid friction pressure with the particle volume fraction was determined. Based on the granular matter theory and results of a direct shear test, the cohesion of the proppant pack was considered in the frictional viscosity model. The results show that the improved solid friction stress model can capture larger angles of the accumulation and settlement profiles, and correctly simulate the process of proppant accumulation.

Damage and fracture are the main causes of structural failure, which have a significant impact on engineering safety. Crack propagation problem is also a fundamental scientific challenge that needs to be solved urgently. In this paper, the relevant theoretical basis for simulating damage and fracture, such as a fracture mechanics model, damage evolution model and numerical calculation methods, such as the finite element method, boundary element method and peridynamics theory, are introduced in the form of literature review. This paper also reviews the commonly used CAE software for structural damage and fracture analysis, including general-purpose finite element programs such as the damage and fracture analysis module that comes with ABAQUS, as well as specialized fracture analysis software, damage tolerance tools, fatigue life analysis tools, etc. The development status of some autonomous CAE software is also discussed. Finally, this paper analyzes some challenges faced by CAE software for damage and fracture simulation, and looks forward to the future development direction of domestic CAE software.

To investigate the evolution of dimpling and the mechanism of interface separation in bimetal clad pipes under external mechanical loading, a stress model was established. The study analyzed the effects of the ratio of diameter to thickness for the inner and outer pipes, forming pressure, initial forming clearance, and operational internal pressure on dent formation and interface separation. Results indicate that interface separation distance and rebound rate correlate positively with the ratio of diameter to thickness for the inner pipes, forming pressure, and initial forming clearance, and negatively with the ratio of diameter to thickness for the outer pipes. Higher operational internal pressure reduces interface separation but increases rebound rate. Internal pressurization of dented pipes decreases interface separation; for instance, under 2-MPa operating pressure, interface separation is 5% less compared with conditions under 2-MPa pressurization. Additionally, the difference in separation between these conditions decreases with increasing pressure. Adjacent dimpling results in increased interface separation in intermediate pipe segments, causing a broader interface separation area compared with isolated dimpling.

The non-isothermal complex flow caused by fluid impacting obstacles is very important to the industrial processes such as nuclear energy utilization. Through coupling various numerical techniques such as the density diffusive term, artificial viscous term, particle shifting technique, a stable and accurate non-isothermal smoothed particle hydrodynamics (SPH) scheme is established, and accurate simulation of non-isothermal complex flow caused by fluid impacting obstacles is realized. Based on the simulation for the non-isothermal flow past a heated cylinder, the non-isothermal dam break past single/multiple obstacles, it is demonstrated that: (1) the developed non-isothermal SPH scheme can not only compute a smooth pressure field and avoid the spurious oscillation of numerical solutions, but also predict accurately the temperature field and the key physical quantities; (2) this SPH scheme can also accurately show the interaction between the heat conduction process and the complex free-surface evolution, and has the capability to simulate non-isothermal complex flows past multiple obstacles.

To study the influence of steel truss web shear deformation on the deflection of steel truss web composite box beams, the beams were first decomposed into a laminated structure composed of top and bottom flanges and a steel truss. A steel truss web shear deformation angle function was introduced to establish an analytical model, and the flexural deformation of a simply supported beam was analyzed as an example. The effective stiffness of the cross-section was determined by combining Euler beam theory and the analytical solution, and the mid-span deflection was calculated using this effective stiffness. The flexural characteristics under different load conditions were analyzed and compared with the Euler beam theory. The influence of structural parameters such as steel truss web diameter, steel truss web wall thickness, and steel truss web inclination angle on the effective stiffness was also examined. The results show that considering steel truss web shear deformation provides an analytical solution closer to the finite element results, with a maximum error of 6.24%. Using the effective stiffness can effectively predict the mid-span deflection, with a maximum error of 3.64% compared with the analytical solution. Among the structural parameters affecting the effective stiffness, steel truss web wall thickness has the greatest influence, followed by steel truss web diameter and steel truss web inclination angle. Additionally, the effective stiffness is positively correlated with steel truss web diameter and steel truss wall thickness but negatively correlated with steel truss web inclination angle.