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.

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.

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.

The radial basis function neural network (RBFNN) is a widely used tool for interpolation and prediction problems. In this paper, we propose to improve the traditional RBFNN by automatically identifying core neurons in the hidden layer, based on the l1 regularization. Our proposed approach will greatly reduce the number of neurons required, which will save the memory and also the computational cost. To determine the radial parameter � in the RBFs, we propose to use the K-fold cross-validation method. Moreover, the principal component analysis (PCA) method is used to reconstruct the distance between samples for high-dimensional data sets. Numerical experiments are provided to demonstrate the effectiveness of the proposed approach.

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.

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.

To meet the needs of industrial production, an improved evolution structural optimization (ESO) method with high efficiency is proposed. The optimized design variables with intermediate density were designed using the windowed evolution structural optimization (WESO) method to increase the stability of the algorithm. The efficient calculation method of the element node sensitivity was established, which realizes the establishment of level set functions, smooth topological design of structures and the updating of design variables. The stability of the proposed algorithm was verified by the Zhou–Rozvany problem, two- and three-dimensional (3D) numerical results. The effectiveness and efficiency of the proposed algorithm was further verified by numerical comparison with other topology optimization frameworks. Lastly, the improved windowed ESO method was applied to the initial configuration design of the double-deck bridge structure, which not only provides guidance for its initial design but also demonstrates the applicability of the method in complex structural systems.

Adhesively bonded joints showcase non-uniform stress distribution, along their length as the load is transferred through layers of dissimilar stiffness. For efficient transfer of loads, the peak interfacial shear stress is required to be engineered. In this study, inspired by electric pulses, the interphase modulus is modified according to square, sinusoidal and triangular pulses. The variation in peak stresses with increased number of pulses up to four is also investigated. The developed analytical model is solved for the interfacial shear stresses as well as the peel stresses, using energy functional approach, through MAPLE software. The abrupt changes in modulus in square pulse graded interphase are observed to create highest interfacial shear stresses among the considered grading profiles. Furthermore, the peak interfacial stresses are observed to increase with increased number of pulses. An effective elastic modulus parameter is defined to indicate the area under the modulus profile curve. The effective modulus is found to be gradually increasing with increase number of pulses in square graded interphase. Whereas, it is constant for sinusoidal- and triangular-graded interphases. A deep machine learning-based physics informed neural network model is developed to quickly solve the developed governing differential equations. Therefore, results from the machine leaning model are compared to the analytical results.

The periodic behaviors of a linear fourth-order difference solution to the Benjamin–Bona–Mahony (BBM)-type equation with time-periodic boundaries are analyzed in this paper. Firstly, we employ a variable transformation to change the original BBM-type equation with time-periodic boundaries into a new BBM-type equation with zero boundaries. We then construct a fourth-order linear finite difference method to discrete the new BBM-type equation. The solvability, convergence, stability and accuracy of the approximating solution are discussed. The computation procedure of the present method is given in detail. Numerical results show that the proposed difference method is reliable and efficient for time-periodic simulation.

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.

In this paper, the explicit solving of pressure Poisson equation and GPU parallelization were employed to improve the efficiency of MPS method, which is one of the mainstream particle methods. The performance of the explicit GPU parallel MPS method is discussed using two-dimensional dam-break and sloshing problems. The reliability and accuracy of the developed algorithm were validated against the results of traditional implicit solving method (based on GMRES) and experiment. In terms of efficiency improvement, compared with the traditional CPU-based serial solver, the explicit GPU-parallelized algorithm greatly reduces the computational time of the pressure Poisson equation. More specifically, the maximum acceleration ratios of 11.486 and 13.89 can be obtained by numerical simulation for 2D dam-break and sloshing problems with different particle numbers.

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.

Artificial neural network (NN) has become one of the most widely used machine learning (ML) models for problems in science and engineering, including the fast-developing artificial intelligence (AI) technology. In training an NN model for a problem, one of the most frequently asked questions is how many neurons or layers of neurons should be used for a given dataset with a number of samples (or data points). This paper provides an answer to this critical question, by presenting a Neurons-Samples Theorem, which states, in short, that the number of neurons should be equal or less than the number of samples used to train the NN.

This paper proposes an interval vibration analysis method for nonlinear systems subjected to uncertain excitations, through which its dynamic displacement response bounds can be calculated effectively. In the proposed method, the uncertain excitations are described using the interval process model developed by the authors in recent years. Firstly, the displacement response of a certain degree of freedom for a nonlinear system at an arbitrary time point is expressed as a function of several standard uncorrelated interval variables by using the interval K–L expansion. Secondly, two constrained optimization models are established for the lower and upper bounds of the displacement response of the nonlinear system at the time point. Thirdly, the efficient global optimization (EGO) method is used to solve the above optimization models, and the dynamic displacement response bounds of the nonlinear system can be further obtained. Finally, the effectiveness of the proposed method is verified by investigating two numerical examples.

Mathematical models for measuring pollutants, by predicting the amount of air quality elements, play an important role to protect the human health. As one of these models, delay Volterra integral equations are applied to simulate a network of sensors with past memory to evaluate the emissions of pollutants in the air. This paper presents a computational method to solve these types of delay integral equations using the discrete Galerkin scheme together with the moving least squares (MLS) approach as basis. The MLS is an effective technique to estimate an unknown function which includes a locally weighted least squares polynomial fitting over a small set of all points. The composite Gauss–Legendre quadrature formula is utilized to compute integrals appearing in the proposed method. Since the scheme is constructed on a local scattered data approximation, its algorithm is attractive and easy to run on a computer with normal features. The error estimation and convergence rate of the method are provided. Finally, numerical examples illustrate the efficiency and accuracy of the new technique and confirm the theoretical results obtained in the error analysis.

Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The assessment of the performance of the adaptive mesh refinement method considers its key features such as drawing closed streamline and identification of singular points, asymptotic planes, and vortex axis. Several illustrative examples of the applications of the 3D mesh refinement method with a multi-level refinement confirm the accuracy and efficiency of the proposed method. Furthermore, the results demonstrate that the adaptive mesh refinement method can provide accurate and reliable qualitative measures of 3D computational fluid dynamics problems.

This paper presents a numerical study on interfacial behavior between hybrid steel and polyvinyl-alcohol fiber-reinforced engineered cementitious composite (HSP-ECC) and concrete. Concrete damage plasticity (CDP) model was used to define the mechanical behavior of HSP-ECC and concrete materials. Interfacial behavior was simulated for as-cast and sandblasted surfaces by adopting traction-separation constitutive model. Key interface parameters were determined by calibration of finite element (FE) modeling results with experimental results. The FE modeling results illustrated the reliability and efficiency of the proposed numerical approach in the prediction of interface bond behaviors between HSP-ECC and concrete for different degrees of surface roughness.

A key difficulty of the conventional unstaggered central schemes for the shallow water equations (SWEs) is the well-balanced property that may be missed when the computational domain contains wet-dry fronts. To avoid the numerical difficulty caused by the nonconservative product, we construct a linear piecewise continuous bottom topography. We propose a new discretization of the source term on the staggered cells, and a novel “backward” step based on the water surface elevation. The core of this paper is that, we construct a map between the water surface elevation and the cell average of the free surface on the staggered cells to discretize the source term for maintaining the stationary solutions. The positivity-preserving property is obtained by using the “draining” time-step technique. A number of classical problems of the SWEs can be solved reasonably.

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%.

Data-driven calibration techniques, consisting of theory-guided feed-forward neural networks with long short-term memory, have previously been developed to find suitable input parameters for the finite element simulation of progressive damage in fibre-reinforced composites subjected to compact tension and compact compression tests. The results of these machine learning-assisted calibration approaches are assessed in a range of virtual open-hole strength tests under tensile and compressive loadings as well as in low velocity impact tests. It is demonstrated that the calibrated material models with bi-linear softening are able to simulate the structural response qualitatively and quantitatively with a maximum error of 9% with regards to experimentally measured open-hole strength values. Furthermore, the highly efficient models enable the virtual analysis of size effects as well as accurate force simulations in quasi-isotropic laminates under impact loading.