Topology optimization (TO) can generate innovative conceptual configurations with shell–infill geometric features by distributing materials optimally within the design domain. However, physics-based topology optimization methods require repeated finite element analysis and variable updating, in which expensive computational cost limits their applications in wider industrial fields, especially for topology optimization for shell–infill structures. Fortunately, the arising of the data-based topology optimization method using deep learning has paved the way to realize real-time topology prediction for shell–infill structures. In this work, a novel and differentiable structural similarity (SSIM) loss function is introduced into the conditional generative adversarial network (cGAN) to construct the SSIM-cGAN model, and the single-channel coding strategy of initial condition is proposed to simplify the inputs of the deep learning model. SSIM-cGAN can generate shell–infill structures in real time after training with a small-scale dataset. The results generated by SSIM-cGAN and cGAN were put together for comparison, demonstrating that the shell–infill structure generated by SSIM-cGAN has lower error than cGAN, and the shell layer and porous infill structures are more integrated.

In this paper, three different smoothed finite element method (SFEM), viz., node-based smoothed finite element method (NS-FEM), face-based smoothed finite element method (FS-FEM) and α-finite element method (α-FEM) are adopted for 3D solids undergoing large deformation. The common feature of all these techniques is the introduction of smoothed strain which is written as a weighted average of the compatible strain field over smoothing domains. The choice of smoothing domain is what differentiates them. The spatial discretization can be based on the simplest and automatically genera-table four-node tetrahedral elements and aforementioned techniques have shown to yield accurate results even on a coarser discretization. To take the advantages of the SFEM, it is beneficial to the FEM community to have it implemented in the widely used Abaqus® software. Such an implementation is challenging because the neighboring SFEM elements are interconnected in the smoothed strain matrices in the elemental level. In this work, the above-mentioned SFEM models are implemented in the commercial software Abaqus using the softwares’ user element (UEL) feature. The challenges during the definition and the assembly of the smoothing domains are effectively addressed in this work. The developed UEL and the associated files can be downloaded from http://github.com/nsundar/3DSFEM. The implementation is validated against benchmark examples and the robustness is demonstrated with complicated real-life problems, viz., tire patch contact with road and simulation of human thumb.

The paper presents a uniformly convergent finite difference method based on the defect correction technique to solve parabolic singular perturbation problems with discontinuous convection coefficient and source. The solution to the problem exhibits interior layer across the discontinuity and demonstrates turning point behavior. The simultaneous presence of perturbation parameters and discontinuity makes the problem stiff. A higher-order method is developed using an implicit difference scheme in time on a uniform mesh and a combination of the upwind difference method and the central difference scheme over an adaptive mesh in space. The method involves iteratively solving increasingly accurate discrete problems by computing and using the defect to correct the approximate solution. Parameter uniform error estimates show uniform convergence of first-order in time and second-order in space. Numerical experiments confirm the accuracy of the proposed scheme and support the theoretical analysis.

This paper presents the modified boundary knot method (MBKM) for solving the homogeneous harmonic type boundary value problems (BVPs). Since no non-singular general solutions are applicable for harmonic-type equations, the general solutions of Helmholtz-type operator with a free parameter λ can be used to approximate the solutions of these problems by adjusting the λ. Compared with the classical boundary knot method (BKM) where the source nodes are the same as the boundary collocation nodes, the MBKM employs the ghost points method, which resets the source points to a disk-like region covering the primary problem area. This modification results in better accuracy without any increase in the computational cost. On the other hand, as the accuracy of the MBKM depends heavily on the parameter λ, the effective condition number (ECN) is first employed to find a proper λ in MBKM. Several 2D and 3D numerical examples are listed to illustrate the superior performance of the MBKM in solving harmonic-type BVPs. The accuracy of MBKM is improved by one to two orders of magnitude compared to the classical BKM. Meanwhile, the validity of the ECN for obtaining a suitable λ for problems under complex geometric regions is also demonstrated.

Bioinspired nacre-like composites have attracted increasing research interests recently. They are typical composites with brick-and-mortar structure and usually employ a combination of hard material and soft material to achieve a good balance between stiffness and toughness. Impact response analysis of such composites is difficult due to their complex structure and interface. In this work, an effective finite element method-smoothed particle hydrodynamics (FEM-SPH) coupling approach is developed for impact response analysis of composite plates with brick-and-mortar structure. In the approach, hard material taking up the bulk of the composite plate is modeled with the SPH method, and soft material forming thin layer structures in the composite plate is modeled with FEM. A coupling algorithm considering failure behavior is proposed to model bonding interfaces between FEM parts and SPH parts. A particle-to-particle SPH contact algorithm is employed to handle contacts between SPH parts, and a penalty-based FEM-SPH contact algorithm is implemented to treat contacts between FEM parts and SPH parts. The developed coupling approach is used to calculate stress wave propagation in two bonded plates of the same material and different materials and a composite plate with brick-and-mortar structure. The accuracy of the coupling approach is validated by comparing the calculated results with those of analytical method and FEM. The coupling approach is then used to simulate the effects of some factors on the impact damage of composite plates with brick-and-mortar structure. The coupling approach can conveniently model the complex structure and bonding interface of the composite plates and is capable of capturing interface failure and fragmentation of the major composition of the composite plates during impact events. It provides a promising alternative for the impact response analysis of brick-and-mortar composite structures.

We apply here a class of substructuring method to improve the performance of linear tetrahedral element used in finite element analysis (FEA). The method is novel and relied on the construction of mesh inside a tetrahedron volume which behaves as an assembly of substructures. The corresponding stiffness matrix of the mesh is assembled using a static condensation procedure which is used further to obtain strain energy from a set of particular displacement vectors. This energy is the key to obtain a so-called energy ratio that will modify the stiffness matrix of a linear tetrahedral element. In the numerical tests, we show that the method can improve the performance of the tetrahedral element to approximate displacement and stress fields from the analytical solutions for cantilever and stress concentration problems, respectively.

Polynomial chaos expansion (PCE) is widely adopted in geotechnical engineering as a surrogate model for probabilistic analysis. However, the traditional low-order PCE may be unfeasible for unsaturated transient-state models due to the high nonlinearity. In this study, a temporal-spatial surrogate model of adaptive sparse polynomial chaos expansions (AS-PCE) is established based on hyperbolic truncation with stepwise regression as surrogate models to improve computational efficiency. The uncertainty of pore water pressure of an unsaturated slope under transient-state rainfall infiltration considering hydraulic spatial variability is studied. The saturated coefficient of permeability ks is chosen to be spatial variability to account for the soil hydraulic uncertainty. The effects of location and time and the performances of AS-PCE are investigated. As rainfall goes on, the range of the pore pressure head becomes larger and the spatial variability of ks has little influence in the unsaturated zone with high matric suction. The pore pressure head under the water table suffers more uncertainty than it in the unsaturated zone. The R2 in the high matric suction zone has a trend of rising first and then falling. Except for the high matric suction zone, the R2 rise over time and they are almost 1 at the end of the time. It can be concluded that the AS-PCE performs better for low matric suction and positive pore pressure head and the fitting effect gradually increases as the rainfall progresses. The quartiles and at least up to second statistical moments can be characterized by the AS-PCE for transient infiltration in unsaturated soil slopes under rainfall.

In this paper, a meshfree approach based on moving kriging interpolation is presented for numerical solution of coupled reaction-diffusion problems. The proposed approach is developed based upon local collocation using moving Kriging shape function. It is truly meshless and having the Kronecker delta property for accurate imposition of boundary conditions. In the proposed model, the weight function is used with correlation parameter treated as the model internal length factor. This produces a local moving kriging method with improved accuracy together with an ease to choose the weight function factor. The method can hence be used in an efficient manner without cumbersome effort for choosing its parameter. The meshless approach is presented for the first time for numerical solution of reaction-diffusion systems. Problems of Turing system and pattern formation in several 2D domains are solved in this study. The efficacy and accuracy of the proposed method for the reaction-diffusion systems in different problem domains are presented in comparison to available exact solution and other numerical methods. It is found that the present method is accurate and effective as a computational procedure for solving reaction-diffusion problems.

Steel fiber-reinforced ultra-high performance concrete (UHPC) material is prone to explosive spalling under elevated temperatures. With the addition of polypropylene (PP) fiber, thermal spalling of UHPC can be mitigated and its fire resistance can be improved. This research investigates the impact resistance of steel and PP fiber-reinforced UHPC slabs after exposure to elevated temperatures, and the structural behavior and damage were compared against normal strength concrete (NSC) slabs. Karagozian & Case concrete (KCC) model was adopted to simulate both NSC and UHPC materials. With consideration of thermal hazards, the material damage, equation of state and strain rate sensitivity were adapted. The validity of this numerical model was evaluated against available experimental results. The numerical model was used to investigate the impact resistance of the reinforced UHPC slabs after exposure to fire hazards. The effect of fire exposure time, impact velocity and impact mass on the resistance of the reinforced NSC and UHPC slabs were analyzed. The simulation results revealed that punching shear failure areas in the NSC slabs were 2.5 times, 3.4 times, 3.0 times and 1.2 times larger than the UHPC slabs after exposure to international standardization ISO-834 standard fire for 1h, 2h, 3h and 4h, respectively. After exposure to the standard fire ISO-834 for 2 h, the punching shear failure on the bottom side of NSC increased 90.9% with the increase in falling height from 1m to 7m, while for the UHPC slabs, the increment was around 67.9%. After exposure to the standard fire ISO-834 for 2h, the punching shear damage of the NSC slabs increased by 72.9% with the punch weight increased from 100kg to 700kg, whereas the damage in the UHPC slabs increased by 53.8%.

This paper represents a new application of Legendre wavelet and interpolating scaling function to discuss the approximate solution of variable order integro-differential equation having weakly singular kernel. So far, this technique has been used to solve variable order integro differential equation. In this paper, it is extended to solve variable order integro differential equation with weakly singular kernel. For this purpose, we derive the operational matrices of Legendre wavelets and interpolating scaling function. The resulting operational matrices along with the collocation method transform the original problem into a system of algebraic equation. By solving this system, the approximate solution is obtained. The convergence and error estimate of the presented method have been rigorously investigated. We also discuss the numerical stability of the method. The numerical result of some inclusive examples has been provided through a table and graph for both basis functions that support the robustness and desired precision of the method.

T lymphocytes have a primary role in both health and disease. Extracellular and intracellular signals determine whether a T-cell activates different cells, divides, or begins apoptosis. The reaction–diffusion process of Ca2+ ions is critical for the initiation, sustenance, and termination of the immunological function of T cell. A nonlinear spatio-temporal dynamics of Ca2+ in T cells is modeled incorporating parameters Sarco/endoplasmic reticulum Ca2+-ATPase (SERCA) pump, Ryanodine receptor, source amplitude, and buffers. A numerical meshless approach using multiquadric radial basis functions (MQRBF), differential quadrature, and Runge–Kutta method is developed for the solution. The results obtained here give better insights of calcium dynamics in T cells.

Steel fiber-reinforced self-compacting concrete (SCFRC) has been developed in recent decades to overcome the weak tensile performance of traditional concretes. As the flexural strength of SCFRC is dependent on the distribution of steel fibers, a numerical model based on Jeffery’s equation was developed in this study for investigating the effects of the concrete flow on the fiber orientation and distribution in SCFRC. This numerical method shows higher computational efficiency than available particle-based methods like SPH and LBM. The influence of casting parameters like casting method, formwork size and casting velocity on the fiber orientation is investigated from the perspective of the flow field of fresh concrete during casting. The simulation results show that the fiber orientation is largely dominated by the concrete flow during the casting process. Importantly, during casting SCFRC beam, fibers tend to be oriented in parallel along the longitudinal direction at the middle section, while they stick up at the end of the formwork due to the upward concrete flow. In addition, the results from parametric studies show that the formwork size and casting method could significantly affect the concrete flow during the casting process, ultimately the orientation of fibers in a SCFRC beam. Furthermore, it indicates that the casting speed needs to be carefully chosen in order to achieve the optimal fiber alignment.

This paper presents the nonsymmetric interior penalty Galerkin (NIPG) finite element method for a class of one-dimensional convection dominated diffusion problems with discontinuous coefficients. The solution of the considered class of problem exhibits boundary and interior layers. Piecewise uniform Shishkin-type meshes are used for the spatial discretization. The error estimates in the energy norm have been derived for the proposed schemes. Theoretical results are supported by conducting numerical experiments. It is established that the errors are uniform with respect to the perturbation parameter �. The uniformness of the error estimates with the perturbation parameter � has also been established numerically for L�- norm.

In this paper, polynomial-based projection type and modified projection-type methods for approximating the solution of Hammerstein integral equations with a kernel of Green’s function type are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and those of superconvergence of the iterated modified projection-type methods are analyzed. A numerical example is given to illustrate the theoretical estimates.

Advances in testing of composite materials in recent years have mostly resulted in the ability to actively characterize the uniaxial response of composites while investigations of multiaxial load cases are rare due to various challenges. One of these challenges is the lack of a suitable specimen geometry for multiaxial testing without unwanted failure modes. Ideally, such geometry should be developed and assessed virtually by means of simulation before costly and time-consuming manufacturing and testing. Therefore, reliable, and efficient simulation methods are required that incorporate the evolution of damage in FRP composites.This study investigates various geometric features virtually of cruciform specimens to test fiber-reinforced composites subjected to in-plane biaxial tensile loadings. The goal is to achieve uniform failure in the gauge region of the specimen due to biaxial stress states and to reduce any premature failure outside the gauge region. Efficient finite element simulation in the commercial software LS-DYNA is used to identify the optimal geometric features.

In this paper, an efficient Jacobi spectral collocation method is developed for multi-dimensional weakly singular volume-constrained nonlocal models including both nonlocal diffusion (ND) models and peridynamic (PD) models. The model equation contains a weakly singular integral operator with the singularity located at the center of the integral domain, and the numerical approximation of it becomes an essential difficulty in solving nonlocal models. To approximate such singular nonlocal integrals in an accurate way, a novel nonlocal quadrature rule is constructed to accurately compute these integrals for the numerical solutions produced by spectral methods. Numerical experiments are given to show that spectral accuracy can be obtained by using the proposed Jacobi spectral collocation methods for several different nonlocal models. Besides, we numerically verify that the numerical solution of our Jacobi spectral method can converge to its correct local limit as the nonlocal interactions vanish.

A simple and efficient iterative method involving Green’s function is presented for solving the general nth-order nonlinear boundary value problems. Existence and uniqueness results for such problems are established using the fixed-point theorems. This guarantees the uniform convergence of the proposed iterative algorithm. The resulting iterative solutions does not contain any unknown constants and automatically satisfy the given boundary conditions. This gives the iterative method much wider applicability in obtaining the analytical or numerical solution of the problem. The performance of the proposed approach is assessed and tested on four examples.

The efficiency and accuracy of the cell-based smoothed discrete shear gap (CS-DSG3) are improved in simplifying the application process of the cell-based strain smoothing technique and redefining the stabilized parameter of Stenberg’s stabilization method, respectively. In the original CS-DSG3, both the smoothed bending strain and the smoothed shear strain are derived by the cell-based strain smoothing technique. This study proves that the smoothed bending strain matrix in the original CS-DSG3 is equal to the unsmoothed bending strain matrix. Theoretically, abandoning the bending strain smoothing operation can improve the efficiency while maintaining the accuracy of the original CS-DSG3. The introduction of Stenberg’s stabilization method can boost the accuracy of shear strain in the original CS-DSG3, whereas the relationships of the stabilized parameter in Stenberg’s stabilization method with the mesh density, the thickness–span ratio, and the boundary condition are still unclear. In this study, the range of the optimal stabilized parameter for different analyses and boundary conditions is determined through the static and dynamic analysis of the plate. The new stabilized parameter is applied to static analyses, free vibration analyses, and frequency response analyses for verification and comparison, which demonstrates that it can significantly improve the accuracy of the CS-DSG3.

Dynamic load identification is a commonly used and quite important approach to obtain the excitation loads of structures in engineering practice. In this paper, a novel dynamic load identification method combining the least squares time element method (LSTEM), wavelet scaling function and regularization method is proposed, which performs a better accuracy and a stronger anti-noise ability. It decomposes the time history of dynamic load into a series of time elements, and approximates the load profile at each time element using wavelet scaling functions. In order to balance the accuracy and efficiency for load identification, an optimal wavelet resolution is then determined. Simultaneously, the least squares time element model is derived which establishes the forward model for computing the wavelet coefficient. Finally, the wavelet coefficients for dynamic load identification are accurately and stably solved by implementing regularization. By this method, on the one hand, the wavelet scaling function and LSTEM improve the identification accuracy, and on the other hand, the integral process in the least squares operation gains the anti-noise ability for the load identification. A numerical example of a roof structure and an experiment of a composite laminate are studied and verify the effectiveness of the proposed method.

In the process of aircraft structural design, the aerodynamic load and inertial load need to be distributed from single loading points to distributed finite element (FE) nodes before strength analysis. The most commonly used loading distribution method is a Multi-Point Arrangement (MPA) method, which introduces a one-dimensional Lagrange multiplier based on the principle of minimum deformation energy, and simplifies the special-shaped 3D surface in aircraft structure to a plane. However, the actual aircraft structure contains a large number of special-shaped surfaces, and the MPA method cannot accurately distribute the loads on these complex special-shaped surfaces, affecting the accuracy of strength analysis. This paper developed a new 3D load distribution method based on multi-dimensional Lagrange multipliers (MDLM), which can simultaneously achieve an efficient and accurate distribution of surface aerodynamic loads and inertial loads in all directions. Typical numerical cases showed that when an aircraft structure model is a plane, this MDLM method converges to the traditional MPA method. For 3D special-shaped surfaces, the average error of this MDLM method is 0.77–2.28%, which is significantly smaller than the average error of the traditional MPA method (3.30–7.40%).