In this paper, two explicit time-marching techniques are discussed for the solution of hyperbolic models, which are based on adaptively computed parameters. In both these techniques, time integrators are locally and automatically evaluated, taking into account the properties of the spatially/temporally discretized model and the evolution of the computed responses. Thus, very versatile solution techniques

It should be noted that in addition to the geometry, constituent material also affects the strength and rigidity of the cylindrical shell, some factors that determine the transient response are its geometry and the constituent material. The capability of piezoelectric materials to adept their properties in reaction to environmental factors including electricity and loading is one of the major reasons

Microfluidics have shown great promise in multiple applications, especially in biomedical diagnostics and separations. While the flow properties of these microfluidic devices can be solved by numerical methods such as computational fluent dynamics (CFD), the process of mesh generation and setting up a numerical solver requires some domain familiarity, while more intuitive commercial programs such as

The flight of a water rocket involves complicated flows such as a gas–liquid two-phase flow in a pressure tank and a jet flow in an ejection hole. It can be applied to various phenomena by developing a method of reproducing and analyzing complicated phenomena. We simulated the flight of a calculation model of a water rocket by computational fluid dynamics. We conducted the simulation to estimate the

A new optimal formulation of the selective cell-based smoothed finite element method using 10-node tetrahedral elements (SelectiveCS-FEM-T10) is proposed for nearly incompressible large deformation problems. SelectiveCS-FEM-T10 is a generic name for S-FEM formulations that apply the selective reduced integration (SRI) and the cell-based S-FEM (CS-FEM) simultaneously to the 10-node tetrahedral (T10)

A mathematical analysis method is employed to solve the bending problem of slip clamped shallow spherical shell on elastic foundation. Using the slip clamped boundary conditions, the differential equations of the problem are simplified to a biharmonic equation. Using the R-function, the fundamental solution and the boundary equation of the biharmonic equation, a function is established. This function

Until recently, linear analysis has been considered sufficient for the static analysis of structural frames. Nonlinear effects, if included, have tended to be considered at the element level rather than at the complete structure level. However, recent changes in codes of practice have been introduced that require a more complete nonlinear analysis to be performed. While these requirements should lead

Based on the Taylor Expansion and constrained moving least square function, a smoothed GFEM (SGFEM) is proposed in this paper for static, free vibration and buckling analysis of Reissner–Mindlin plate. The displacement function based on SGFEM is composed of classical linear finite element shape function and nodal displacement function, which are obtained by introducing the gradient smoothed meshfree

The current paper presents a perturbation-based stochastic eigenvalue buckling analysis of thin plates using element free Galerkin method. Spatial variation in Young’s modulus is modeled as a homogeneous random field and moving least square-based shape function method is employed for discretizing the random field. Perturbation method is used to evaluate the statistics of buckling loads. Numerical examples

Macroscale mesh sensitivity and RVE size dependence are the two major issues that make the conventional homogenization techniques incapable of modeling the softening behavior of quasi-brittle materials. In this paper, a new continuous–discontinuous multiscale modeling approach to failure is presented. Inspired by the classical crack band model of Bazant and Oh (1983), this approach is built upon an

In recent decades, growing efforts have been devoted to coupling the Computational Fluid Dynamics (CFD) and the Discrete Element Method (DEM), i.e., CFD-DEM coupling methods, to account for particle–fluid interactions. However, it remains a challenging task for the well-known Immersed Boundary Method (IBM) belonging to the resolved CFD-DEM methods to improve the computational efficiency of large particles

Laser Powder Bed Fusion (LPBF) is an additive manufacturing method that manufactures high density and quality metal products. We present a coupled grain growth and heat transfer modeling technique to understand the materials microstructure evolution in metals during the cooling process of LPBF. The phase-field model is combined with a transient heat transfer equation to simulate the solidification

The dynamic characteristics of a hub-functionally graded material beam undergoing large overall motions are studied. The deformation field of the flexible beam is described by using the assumed mode method (AMM), the finite element method (FEM) and the point interpolation method (PIM). Assuming that the physical parameters of functionally graded materials follow certain kind of power law gradient distribution

The paper proposes a novel automatic adaptive recovery stress edge-smoothed finite element method (ES-FEM) that determines the maximum load capacity of inelastic structures at plastic collapse. This approach performs solely a series of elastic ES-FEM analyses with systematic modulus variations (considering the influences of stress singularity) to converge the collapse load solutions. The smoothed C0-continuous

In traditional structural reliability analysis, the uncertainties, such as loads and strengths, are considered as random variables with specific probability distributions. When the information is insufficient, it is difficult to obtain the distribution functions. Hence, experts are usually asked to estimate the belief degrees. Uncertainty theory is a branch of mathematics used to model the belief degrees

A two-dimensional (2D) boundary element method (BEM) is proposed by replacing traditional polynomial interpolation with one-dimensional (1D) scaling functions of B-spine wavelet on the interval (BSWI). Potential problem and elasticity problem are investigated by BSWI BEM. For these two problems, the boundary variables represented by coefficients of wavelets expansions are transformed from wavelet space

Under the low-velocity impact conditions, in order to study the contact load variation law of the ellipsoid elastic bodies, an elastic–plastic contact analysis model of rough ellipsoid surfaces is provided based on elastic–plastic fractal theory. A spherical elastic–plastic fractal model considering friction factors is established, and the spherical diameter density distribution function and elastic

In the field of structural dynamics, spectral finite elements are well known for their appealing approximation properties. Based on a special combination of shape functions and quadrature points, a diagonal mass matrix is obtained. More recently, the so-called optimally blended spectral element method was introduced, which further improves the accuracy but comes at the cost of a non-diagonal mass matrix

Most of the current non-probabilistic reliability methods are applicable for an individual component of a structure. However, a system consisting of interconnected components is involved in many engineering problems and its non-probabilistic reliability analysis remains a major challenge. In this paper, a non-probabilistic reliability method using upper and lower bound techniques is proposed for a

A novel numerical method named element differential method (EDM) is first presented to solve linear and nonlinear static electromagnetic problems. The main idea of this method is to use the direct differentiation formulation of the shape functions of Lagrange isoparametric elements to evaluate geometry and physical variables. A new collocation method is proposed to establish the system of equations

In this paper, a new algorithm is presented to solve the nonlinear second-order differential equations. The approach combines the Quasi-Newton’s method and the multiscale orthogonal bases. It is worth mentioning that the convergence of Newton’s method is verified for solving the nonlinear differential equations. The uniform convergence of the numerical solution as well as its derivatives are also proved

The ultimate goal of this study is to implement a fixed point iterative scheme for the numerical solution of an extended class of nonlinear, nonlocal, elliptic boundary value problems. The method is based on applying well-known fixed point procedures such as Mann’s and Picard’s to a tailored linear integral that is expressed in terms of a Green’s function. A proof of convergence that utilizes the contraction

This work focuses on the derivation of the local variant of the singular boundary method (SBM) for solving the advection-diffusion equation of tracer transport. Localization is based on the combination of SBM and finite collocation. Unlike the global variant, local SBM leads to a sparse matrix of the resulting system of equations, making it much more efficient to solve large-scale tasks. It also allows

In this work, we report on the formulation and detailed stability analysis of a dynamic multi-scale scheme involving two different local computational strategies for modeling of elastic wave propagation. The coupled model involves the Local Interaction Simulation Approach and Cellular Automata for Elastodynamics, however the presented analysis approach is general and applies to other numerical techniques

The aim of this paper is to investigate the application of radial basis function-generated finite difference (RBF-FD) methods for convection–diffusion partial differential equations (PDEs) on a sphere. In the application of RBF-FD method, choosing a reasonable value of shape parameter is important to the computation of PDEs. The work is devoted to the numerical study of the range of near optimal shape

The periodic flows, such as vortex shedding and rotating flow in turbomachinery, are very common in both scientific and engineering fields. However, high-fidelity numerical simulations of unsteady flows are usually time-consuming, particularly when varying flow parameters need to be considered. In this paper, a novel nonintrusive parametrized reduced order model (PROM) approach for prediction of periodic

Variable stiffness (VS) composite structures can greatly increase the composite designability and thus have attracted much attention in recent years. This paper focuses on the maximization of load carrying capacity of VS composite cylinders under different loading cases, and the multi-objective optimization method is used to get the optimal results. First, the VS composite cylinder is optimized under

In order to better understand the interfacial debonding behavior of pipe joints during the whole loading process, an analytical solution for the full-range behavior of adhesively bonded pipe joints under combined thermal and mechanical tensile loadings is presented in this paper. The solution was developed based on a simplified rigid-softening bond–slip model, and two cases with different softening

This paper presents the node-based smoothed finite element method with linear strain functions (NS-FEM-L) for solving contact problems using triangular elements. The smoothed strains are formulated by a complete order of polynomial functions and normalized with reference to the central points of smoothing domains. They are one order higher than those adopted in the finite element method (FEM) and the

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the

Linear equation solvers require considerable computational time in many computer simulation methods, such as the stress analysis using the finite element method (FEM), or the fluid dynamics using an implicit time integration scheme. Because of their favorable nature to modern supercomputers, Krylov-type linear equation solvers have become dominant. Krylov-type solvers are usually used with preconditioners

An efficient dynamic load identification method for nonlinear structures is proposed. Assuming that the nonlinear elements of a structure can be separated, or the structural kinetic equation can be available, the whole structural damping and stiffness matrices can be divided into linear and nonlinear sub matrices. Regarding the effects of the nonlinear elements on the linear ones as dynamic load constraints

Changes in the thermomechanical properties of fiber-reinforced concrete (FRC) exposed to fire are fundamentally affected by the type and volume fraction of fibers. Because the loss of FRC load-bearing capacity is mainly caused by structural damage, a new numerical procedure based on a modified method of discontinuous boundary elements (DBEM) is proposed, which is modified to include thermomechanical

This work is about a heat transfer phenomenon in relation to the periodically laminated composite. The specific type of thermal loading, analyzed in this paper, require formulation of Robin boundary conditions. To consider a layered structure of analyzed composite, the tolerance averaging technique is used. This method allows to take into account a thickness of the layers and obtain the equations with

Various types of machinery are not a continuous whole, but are assembled from various parts according to specific requirements. The surfaces that contact each other between different parts are often called mechanical joints. The stress/displacement field of the mechanical joint structure is the basis for predicting the mechanical properties of the assembly, optimizing the structure and the assembly

In this paper, one of the variants of the smoothed finite element method, α-FEM is adopted for hyperelastic material with large deformation and contact nonlinearity in two dimensions. The salient feature of the α-FEM is that it is stable and this is accomplished by using the scale factor α∈[0,1] to combine the compatible finite element method and the node-based smoothed finite element method. The framework

The Vlasov equation describes the temporal evolution of the distribution function of particles in a collisionless plasma and, if magnetic fields are negligible, the mean electric field is prescribed by Poisson equation. Eulerian numerical methods discretize and directly solve the Vlasov equation on a mesh in phase space and can provide high accuracy with low numerical noise. In this paper, we present

Recently, wavelet theory has become a well recognized promising tool in science and engineering field; especially, wavelets are successfully used in fast algorithms for easy execution. In this paper, we developed wavelet lifting scheme using orthogonal and biorthogonal wavelets for the numerical solution of dynamic Reynolds equation for micropolar fluid lubrication. The numerical results gained through

The main objective of this research is to propose a multidisciplinary approach for the development and design of Computer Numerical Control (CNC) machine tools using numerical optimization methods combined Multi-Body Dynamic (MBD) analysis and to control design co-simulation. Metamodels based Sequential Approximate Optimization (SAO) for the co-simulation optimization problems are developed. The metamodels

Support vector regression (SVR) has been widely used to reduce the high computational cost of computer simulation. SVR assumes the input parameters have equal sample sizes, but unequal sample sizes are often encountered in engineering practices. To solve this issue, a new prediction approach based on SVR, namely as high-low level SVR approach (HL-SVR) is proposed for data modeling of input parameters

Crack initiation and propagation are the two key issues of concern in the geotechnical engineering. In this study, the numerical manifold method (NMM) is applied to simulate crack propagation and the topology update of the NMM for multiple crack propagation is studied. The crack-tip asymptotic interpolation function is incorporated into the NMM to increase the accuracy of the crack-tip stress field

An important technological problem is solved by numerical methods. Doping of silicene with phosphorus allows changing the morphology of the walls of the silicene channel without reducing their strength. The structure of lithium packings in the channels is studied in detail. The distribution of normal stresses in the walls of the channel before lithium intercalation and after complete lithium filling

In this paper, we give some refinements of Simpson’s rule in cases when it is not applicable in its classical form i.e., when the target function is not four times differentiable on a given interval. Some sharp two-sided inequalities for an extended form of Simpson’s rule are also proven.

One of the most important tasks in the numerical analysis of the fracture problem is to achieve a high-precision approximation of the singular stress fields at crack tips. Partially or fully enriched basis functions are often used as enhancements on the whole problem domain or just near the crack tips when constructing the meshless shape functions to simulate the singularity fields at crack tips, namely:

In this paper, we present novel cell-centered finite element methods for the convection-dominated convection–diffusion problems on the general meshes. The proposed schemes can be constructed from a general mesh by building with a dual mesh and its triangular sub-mesh. Moreover, the schemes are based on piecewise linear functions combined with two upwind techniques on the dual sub-mesh in order to stabilize

In this paper, a new family of composite implicit time schemes is developed to overcome some shortcomings of the existing composite schemes. In the development, unconventional time approximations are used for the displacement and velocity vectors. The algorithmic parameters of the approximations are optimized to have improved numerical characteristics. This study also explains some difficulties of

In this paper, we propose the two-level defect-correction stabilized finite element method based on pressure projection for solving the incompressible Navier–Stokes equations. The new method combines the two-level method and the defect-correction strategy with the stabilized method based on pressure projection. It has the good properties of these three methods, such as high efficiency, good stability

Numerical solutions to heat conduction problems involving phase change have traditionally been obtained using the grid-based finite difference or finite element methods. However, due to the unique mathematical form of the equations and the limitations of the grid algorithm, difficulties may arise in solutions. In this study, smooth particle hydrodynamics (SPH) method is used to calculate heat conduction

During the service period of ancient building structures, due to the cumulative development of local damage to load-bearing members such as columns, the structural strength and stiffness will decrease, which may lead to catastrophic accidents. The traditional damage recognition method based on modal parameters is sometimes not effective. In this study, the vibration analysis combined with the relative

In this paper, the dynamic response of piezoelectric structures under hygrothermal environment is studied by using cell-based smoothed finite element method (CS-FEM). Ignoring the influence of temperature and moisture on the response of elastic matrix, we derive the basic equations of the piezoelectric materials under hygrothermal environment. Then the CS-FEM equations of piezoelectric problem are

This paper presents a cell-based smoothed finite element method (CS-FEM) for solving two-dimensional contact problems with the bi-potential formulation. The contact force and the relative displacements on the contact surface are coupled with each other. The Uzawa algorithm, which is a local iterative technique, is used to solve the contact force. The classic Coulomb friction rule and a unilateral contact

Commonly, variance-based global sensitivity analysis methods are popular and applicable to quantify the impact of a set of input variables on output response. However, for many engineering practical problems, the output response is not single but multiple, which makes some traditional sensitivity analysis methods difficult or unsuitable. Therefore, a novel global sensitivity analysis method is presented

The current level of numerical methods of gas dynamics makes it possible to optimize compressors using 3D CFD models. However, the methods and means are not sufficiently developed for their wide application. This paper describes a new method for the optimization of multistage axial compressors based on 3D CFD modeling and summarizes the experience of its application. The developed method is a complex

A novel evaluation study of the most appropriate round function for nearest neighbor image interpolation is presented. Evaluated rounding functions are selected among the five rounding rules defined by the Institute of Electrical and Electronics Engineers IEEE 754-2008 standard. Both full- and no-reference image quality assessment metrics are used to evaluate the influence of rounding functions on

In this work, a face-based smoothed point interpolation method (FS-PIM) is formulated for three-dimensional (3D) thermal elastic-plastic analysis of structures. For this method, field functions are approximated using second order PIM shape functions and the face-based smoothing domains are used to perform the numerical integration. The material properties are considered to be temperature-dependent

The scaled boundary finite element method (SBFEM) has obvious advantages in simulating both finite and infinite domains. However, the present high-order transmission boundary of SBFEM has a problem in numerical stability, especially for 3D fluid–structure interaction (FSI) problems. In this paper, a modified method is put forward to improve the numerical stability of the high-order transmission boundary

The improved reflectance prediction model for printing dot was established with the Monte Carlo method. Reflectance model is a useful approach to predict and control printing quality, which was widely used in color duplication field. The Monte Carlo prediction model for printing dot is a simulation model, satisfying industrial virtual reality needs, which could simulate reflectance data as well as

An iterative domain decomposition method is proposed for numerical analysis of 3-dimensional (3D) linear magnetostatic problems taking the magnetic vector potential as an unknown function. The iterative domain decomposition method is combined with the preconditioned conjugate gradient (PCG) procedure and the hierarchical domain decomposition method (HDDM) which is adopted in parallel computing. Our

In this paper, a cell-based smoothed finite element method using the arbitrary n-sided polygonal element (CS-FEM-Poly) is developed to solve fluid mechanics problems. A stabilization method, characteristic-based split coupled with stabilized pressure gradient projection (CBS/SPGP), is employed to deal with numerical oscillations for CS-FEM-Poly. We validate CS-FEM-Poly and test its numerical behaviors

Lagrangian particle-based methods have opened new perspectives for the investigation of complex problems with large free-surface deformation. Some well-known particle-based methods adopted to solve non-linear hydrodynamics problems are the smoothed parti- cle hydrodynamics (SPH) and the moving particle semi-implicit (MPS). Both methods model the continuum by a system of Lagrangian particles (points)