A novel hybrid approach for transient heat conduction analysis is proposed in this paper, which couples a fully smoothed finite element formulation with a spectral integration technique to enhance computational efficiency and accuracy. Starting from an initial triangular mesh, a smoothing domain is constructed for each edge by connecting its two vertices to the centroids of adjacent triangular elements. Unlike the conventional gradient smoothing technique, which is limited to domain integrals involving shape function derivatives, the quasi-weak form of the smoothed integral handles domain integrals of the shape functions themselves. This transformation converts all domain integrals in the heat conduction and heat capacity matrices into boundary integrals over the smoothing domains, eliminating the need for coordinate mapping and Jacobian matrix calculations. The semi-discrete heat conduction equation is solved using a spectral integration technique, which achieves arbitrary orders of accuracy while significantly improving computational efficiency and stability. Numerical examples demonstrate the capability and accuracy of the proposed method in solving transient heat conduction problems.

This paper presents a novel numerical framework for upper bound limit analysis by integrating the numerical manifold method (NMM) with second order cone programming. By decoupling the mathematical cover from physical boundaries through its dual cover system, the NMM eliminates the need for mesh conformity, efficiently addressing complex geometries. The velocity field is discretized using shape functions constructed by combining weight functions on mathematical patches with local velocity approximations on physical patches, where the degrees of freedom serve as optimization variables. With the plastic dissipation power expressed in terms of such a kinematically admissible velocity field, the upper bound limit analysis problem is formulated as a nonlinear programming problem subject to the external work rate normalization constraint and the incompressibility condition, which is treated differently for plane stress and plane strain states. The resulting non-smooth optimization problem is further expressed as the minimization of a sum of Euclidean norms, cast as a second order cone programming problem, and solved using a primal–dual interior-point algorithm to directly obtain the limit load multiplier and the associated kinematically admissible velocity field. The strong performance of the proposed upper bound limit analysis method is validated through several benchmark examples under both plane stress and plane strain states, demonstrating its capability to effectively eliminate volumetric locking.

This paper presents a novel algorithm for dynamic elastoplastic analysis based on the cell-based smoothed interpolating element-free Galerkin (CS-IEFG) method. The problem domain is discretized into triangular background cells, each subdivided into multiple smoothing domains. Shape functions are constructed using the interpolating moving least squares (IMLS) method, which ensures the kronecker delta property and thus allows straightforward enforcement of essential boundary conditions. Through a generalized gradient smoothing operation, the conventional domain integration required for constructing stiffness matrices and strain fields is transformed into boundary integrals over the smoothing domains, thereby completely eliminating the need for shape function derivatives. Plastic strain evolution follows the associated flow rule, with isotropic hardening representing the increase in yield strength due to plastic deformation. The resulting dynamic nonlinear system is solved using an unconditionally stable Newmark time integration scheme combined with the Newton–Raphson iterative method. Numerical examples demonstrate the validity, accuracy, and effectiveness of the proposed method for dynamic elastoplastic analysis.

Conventional finite element methods face significant challenges in the lower bound limit analysis of thin plates, primarily due to the strict C1 continuity requirement and high sensitivity to mesh distortion. To overcome these issues, this study proposes a novel lower bound limit analysis method for thin plates based on a generalized conforming element developed using the quadrilateral area coordinate (QAC) method. Because the consistently linear transformation between the area and Cartesian coordinates, the proposed element maintains high numerical accuracy even under severely distorted meshes. The principle of virtual work is then employed to weakly enforce the equilibrium conditions for the self-equilibrated moment field. On this basis, a lower bound analysis framework is established following the lower bound theorem of plastic limit analysis, which maximizes the limit load multiplier subject to two essential constraints, namely the equilibrium conditions of a self-equilibrated moment field and the von Mises yield criterion. The von Mises yield criterion is reformulated into second-order cone constraints, thereby leading to a standard second-order cone programming (SOCP) problem that is efficiently solved using the primal-dual interior-point method as implemented in MOSEK. Numerical results validate the rationality and effectiveness of the proposed method, demonstrating superior accuracy and robustness even for severely distorted meshes.

In this paper, an effective method based on the extended finite element method (XFEM) and the back propagation neural network (BPNN) to predict fatigue crack length and residual fatigue life is presented for internal cracks. The XFEM is used to obtain the simulation data of the crack growth model, including the displacement of boundary response points, service cycles, crack length, and residual life. Based on the XFEM simulation data, BPNN is used to construct a fatigue crack prediction model. It is achieved that, by knowing the service cycles and the displacement of the boundary response point, the crack growth length and residual life under different operating conditions can be predicted. This method provides a novel way to predict crack length and fatigue life in practical engineering problems. Two numerical examples of central crack and single edge angled crack are given to evaluate the accuracy of the BPNN prediction method. The results show that the average relative error for predictions of different crack growth lengths is within 2%, and the average relative error for residual fatigue life prediction does not exceed 6.5%. This indicates that the proposed method can effectively predict fatigue crack growth under different operating conditions.

This paper proposes a hybrid numerical framework that integrates the spectral integration technique into the numerical manifold method for accurate and efficient elastodynamic analysis. Based on Gaussian quadrature and orthogonal polynomial expansions, the solution accuracy can be systematically improved with an increase in the number of Gaussian points, and in principle, arbitrary-order temporal discretization accuracy can be achieved. A major strength of this approach lies in overcoming strict time step limitations, thus ensuring high accuracy and stability even with coarse temporal discretization. Spatial discretization of the dynamic equilibrium equation is performed within the numerical manifold method, where the dual cover system decouples the mathematical cover from the physical boundaries, offering superior flexibility in addressing problems with complex geometries. A series of benchmark examples involving transient loading and complex geometries are investigated. The results verify the applicability of the proposed method under diverse mechanical conditions, demonstrate its superior performance in terms of solution accuracy and computational cost, and thus confirm it as a competitive alternative for elastodynamic analysis.

In this study, a tensor decomposition based reduced-order model of the space-time boundary mapped collocation (BMC-ST) method is proposed for analyzing three-dimensional transient heat conduction problems. The core innovation lies in transforming the three-dimensional spatio-temporal domain into a four-dimensional orthogonal computational space, where the approximation model is constructed by the tensor products of independent one-dimensional moving least squares (MLS) shape functions along the spatial coordinates (X, Y, Z) and the temporal axis (T). This unique formulation fundamentally eliminates the need for complex spatial meshing and traditional time integration schemes, which are major bottlenecks in conventional numerical methods. The BMC-ST method maintains high accuracy across an exceptionally wide range of time steps (from 2.5 & times; 10-3 s to 2 & times; 105) and achieves up to an 80-fold improvement in computational efficiency over the finite element method (FEM) for nonlinear problems. Moreover, by employing the Adaptive Compact Support Domain (ACSD) technique, the BMC-ST method preserves a banded sparse matrix structure and the Kronecker delta property, facilitating efficient imposition of boundary conditions even with non-uniform discretization. Numerical experiments, including the three-dimensional nonlinear problems with complex geometries and Functionally Graded Materials (FGMs), demonstrate the high computational accuracy and efficiency of the proposed method, establishing the BMC-ST potential for large-scale engineering applications.

In this paper, a generalized conforming element formulated by the quadrilateral area coordinate method is developed for upper bound limit analysis of thin plates. This element can prevent loss of accuracy in severely distorted meshes since the transformation between the area and Cartesian coordinates is always linear. Once the deflection field is approximated and the upper bound theorem applied, upper bound limit analysis of thin plates can be formulated by minimizing the dissipation power subject to a set of equality constraints. In order for overcoming the difficulties caused by the nonsmoothness of the goal function, a direct iterative method is utilized to solve this optimization problem, which distinguishes the rigid zones from the plastic zones at each iteration. Numerical examples show that the proposed method for upper bound limit analysis of thin plates is reasonable and effective and possesses the advantages of high accuracy and reliability even for severely distorted meshes.

This paper describes an efficient semi-analytical technique, the interpolating element-free Galerkin scaled boundary method (IEFG-SBM), to address the waveguide eigenvalue problem. A weighted residual method, combined with a coordinate transformation between scaled and cartesian coordinates, is utilized to convert the governing partial differential equations for the waveguide eigenvalue problem into a set of first-order ordinary differential equations related to the dynamic stiffness matrix in wavenumber domain. Through using the continued fraction technique and incorporating auxiliary variables, a generalized eigenvalue equation with respect to the cutoff wavenumber of waveguide is derived. Only a set of boundary scattered nodes are required and the improved interpolating moving least-squares (IIMLS) method is employed to construct shape functions in the circumferential direction. The IIMLS method avoids the use of singular weight function and its shape function exhibits the delta function property. Numerical examples are provided to demonstrate that the present method attains high computational accuracy with fewer nodes, effectively handling complex geometries.

This paper proposes a novel numerical method based on the cell-based smoothed radial point interpolation method (CS-RPIM) combined with second-order cone programming to perform lower bound limit analysis of elastic-perfectly-plastic thin plates, using only deflection as nodal variable. The problem domain is initially discretized using a simple triangular background mesh, where each triangular cell is subsequently subdivided into multiple smoothing domains. Shape functions are formulated using the radial point interpolation method, allowing direct imposition of essential boundary conditions for deflection. Rotational constraints are conveniently handled through the construction of smoothed curvatures. By utilizing a generalized gradient smoothing technique, complex domain integrals are simplified into boundary integrals over the smoothing domains, thus eliminating the need to compute second-order derivatives of the shape functions. The virtual work principle is employed to enforce the equilibrium conditions for the self-equilibrated residual moment field in a weak sense. The von Mises yield conditions are expressed as conic constraints and the resulting optimization problems are solved using highly efficient primal-dual interior point solvers. Numerical examples demonstrate that it is feasible and effective to conduct lower bound limit analysis of thin plates using the proposed CS-RPIM and second-order cone programming.

This paper presents a novel fully edge-based smoothed finite element method for free vibration analysis of functionally graded plates, incorporating a quasi-weak form of smoothed integral within an edge-based finite element method framework. Employing first-order shear deformation plate theory, the present method accounts for transverse shear strain and rotary inertia effects while addressing exponentially graded material properties along the plate thickness. The formulation integrates a three-node Mindlin plate element (MIN3) with a shear stabilization technique to prevent shear locking. The quasi-weak form of smoothed integral necessitates the evaluation of indefinite integrals for shape functions, effectively tacking domain integrals related to the shape functions without partial derivatives. By applying both quasi-weak form of smoothed integral and strain smoothing technique, all domain integrals in stiffness and mass matrices are converted into boundary integrals over smoothing domains. Therefore, isoparametric mapping and computing of Jacobian matrix are completely eliminated throughout the solution process. The natural frequencies obtained using the present method are in good agreement with those reported in the literature, highlighting the versatility of the present method for free vibration analysis of functionally graded plates. Notably, the present method demonstrates advantages in eliminating shear locking and reducing sensitivity to mesh distortion.

In this study, the boundary singular method (SBM) is extended to deal with the vibro-acoustic simulation of poroelastic structure. The SBM adopts the fundamental solutions of governing equations rather than simple polynomials to approximate the numerical solutions. By virtue of the fundamental solutions, the SBM avoids the domain discretization, and discretizes the domain of interest into boundary points. In vibro-acoustic problems, the SBM formulates the numerical solutions for the poroelastic structure and the acoustic domain, respectively, through linear combinations of the fundamental solutions to the governing equations. Then the coefficients in the SBM formulations are solved via the boundary conditions and coupling interface conditions, where the singular terms caused by the fundamental solutions are replaced with finite values named origin intensity factors. Different numerical experiments are carried out to illustrate the validity and performance of the proposed methodology. It should be noted that no extra modifications are required for the SBM in the application to the infinite and semi-infinite cases.

In this work, an edge-based strain smoothing technique and a quasi-weak form of smoothed integral are integrated with the three-node Mindlin plate element (MIN3) to develop the fully edge-based smoothed three-node Mindlin plate element (FES-MIN3) for static and free vibration analyses of Reissner-Mindlin plates. To overcome the limitations of the conventional strain smoothing technique, which can only handle the domain integral corresponding to partial derivatives of shape functions, a quasi-weak form of smoothed integral is also introduced. This approach effectively addresses the domain integral related to the shape functions without partial derivatives. Unlike the standard smoothing technique, the quasi-weak form requires the computation of indefinite integrals of shape functions and does not reduce the continuity requirements for the shape functions. All domain integrals in stiffness and mass matrices can be transformed into boundary integrals over the smoothing domains, completely eliminating the need for coordinate mapping and Jacobian matrix calculations. The FES-MIN3 significantly enhances solution accuracy through the softening effect of edge-based strain smoothing and effectively mitigates the issue of shear locking. Numerical examples demonstrate the superior accuracy of FES-MIN3 to many existing elements, as well as its excellent performance in resisting mesh distortion.

In this paper, a linear smoothing scheme over eight-node Reissner-Mindlin plate element under the framework of the CS-FEM is employed to buckling analysis of laminated composite plates based on the first-order shear deformation theory. The modified stain matrix is computed by the divergence theorem between the nodal shape functions and their derivatives using Taylor's expansion. Isoparametric mapping and the computation of interior derivatives of shape function is not required in the proposed method, furthermore, all the computation are based on the global Cartesian coordinates. Some numerical examples are given at the end to demonstrate that the present method has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes.

This article aims to evaluate the effects of mesh size change on the mechanical properties of GFRP laminates, via low-velocity impact and compression-after-impact (CAI) test, and the failure mechanism was analyzed. Through vacuum-assisted resin infusion, wire meshes with different mesh numbers and wire diameters were incorporated into GFRP. Based on response history and failure morphology, the results show that the addition of wire mesh can disperse the incident energy from the impact center to the outer region, thereby improving the impact resistance of GFRP. It is worth noting that increasing the number of mesh could improve the stiffness of the panels and enhance their ability in CAI events compared with increasing the diameter of wires, their failure evolution was presented from the perspective of digital image correlation (DIC). For example, the maximum displacement of 0.50-40 J decreased by 10.6% from 2.5 to 2.26 mm compared with 20-60 J.

The singular boundary method (SBM) is a boundary-only meshless collocation method, but it is not applicable to solve multi-material cases directly with closed-form fundamental solutions. In this study, a semi-analytical boundary-only approach, multi-domain SBM (MD-SBM), is firstly formulated to study the dynamic analysis of multilayered saturated porous media. Firstly, the domain is divided into several subdomains with the consistent material. Then, the singular boundary method (SBM) simulates the dynamic response in each subdomain via a linear combination of fundamental solutions. The source singularity issue is removed by the origin intensity factors (OIFs) rather than singular integrals in the BEM. Finally, the SBM solutions in each layer are coupled by the continuity and compatibility conditions on the interface boundaries between adjacent layers. The SBM does not require domain discretization and desingularizes the source singularity with simple formulas. Thus, it is easy to implement. The MD-SBM is tested to both finite and semi-infinite cases to illustrate its accuracy and feasibility. It is worthnoting that the closed-form fundamental solutions can be directly applied to the semi-infinite cases without requiring additional modifications.

将插值型无单元Galerkin法与时域自适应精细算法相结合,提出一种求解弹性动力学问题的方法.通过时域分段展开,将时空耦合的初边值问题转换为一系列的空间边值问题,进而采用加权残值法推导递推形式的插值型无单元Galerkin法求解方程.该方法不仅能方便地直接施加本质边界条件,并且可以避免时间步长较大造成的精度损失.数值算例给出的结果验证了该方法的有效性.

为了顺应土木行业发展,实现复合型人才培养目标,华东交通大学土木建筑学院应用BIM技术进行了土木类联合毕业设计的探索与实践.文章介绍了联合毕业设计的实施框架,详细说明了多专业分工与协作的内容和方法,提出了联合毕业设计成绩评定和学习效果调查的方式,并结合三年的经验总结,对出现的困难和取得的成效进行了探讨.实践表明,BIM技术在联合毕业设计中的应用,不仅能提高师生工作效率,提升作品质量,而且能使选题与工程实际结合更加紧密.

In this paper, a 2.5D singular boundary method (SBM) in conjunction with the direct differentiation method (DDM) and adjoint variable method (AVM) are formulated for the sensitivity analysis of 3D longitudinally invariant structures. The assumption of a constant cross-section in the longitude direction enables it possible to decouple the 3D system into 2D problems at every wavenumber, and thus makes it a 2.5D-problem. The 2D sensitivity problem is solved by a boundary-type method, SBM. The SBM solves a problem with a linear combination of the fundamental solutions with respect to boundary collocation points. The fundamental solution makes the SBM available for exterior problems without the artificial truncated boundary. The source singularity issue of fundamental solution is overcome by a simple analytical formula and its derivatives. Numerical experiments present the accuracy, efficiency and feasibility of the proposed methods, and indicate that the proposed methods can be considered as an effective alternative in 3D problems with a longitudinally invariant cross-section.