International Journal of Computational Methods

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 dot shape image. This paper mainly focuses on improving the existing reflectance model for printing dot with simulation program, expanding dot simulation area from one single dot to nine dots. The results showed that the reflectance value closely approached the measured value with high dot area in particular and the correlation coefficient improved to 0.924. 100,000 times was shown to be the optimal number of simulated photon under regular printing condition. The expanding simulation area could significantly eliminate interactive influence among the dots. The photon distribution and dot shape could be sufficiently simulated through this model, providing a reference for quality control. The results indicate that the improved reflectance model increased the reflectance accuracy and could further promote optical study about color duplication.

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 dynamic method is used to analyze the damage of the wooden columns of the ancient building. The dynamic damage identification experiment was performed on a single wooden column. The effects of compressing the wooden column, crack length, and application of axial pressure on the natural frequency of the wood column were explored. The natural frequency of the wood column was determined by data acquisition and signal processing (DASP) software, and the damage of the component was evaluated by analyzing the change in the natural frequency obtained under different states. Results of the relative dynamic method showed that the damages can be evaluated by observing the change in the natural frequency. However, determining the damage position and the damage form was impossible. Then the mode shapes at different frequencies were obtained by processing the time domain signal, Fast Fourier Transform (FFT) calculation, and simultaneously using the Eigensystem Realization Algorithm (ERA). It is able to detect the damage of the ancient building components without damage, adding experiments to verify it, and enriching the application of the relative dynamic method theory. According to the variation law of the vibration mode animation, the location of the crack is generally concluded.

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 deduced based on the constitutive equation of the material. The improved Newmark scheme is used to solve the transient response of this problem. Several numerical examples are given to illustrate the advantage of CS-FEM in dealing with piezoelectric materials in hygrothermal environment. Results of this study provides some ideas for the design and manufacture of piezoelectric smart structures in hygrothermal environment.

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 relationship are considered. There is no need to select any user-defined parameter in the whole process. Three contact states are investigated accurately, which can be stated as sticking, separating and sliding, respectively. The CS-FEM is performed with six different kinds of smoothing domains which are constructed by dividing the background element into different regions. Only boundary integrations instead of domain integral are required in the calculation, and no coordinate mapping is needed. Three numerical examples are presented to verify the effectiveness of the method. The effect of the friction coefficient for the contact is also investigated. All the obtained numerical solutions agree well with the reference values. The results produced by the CS-FEM are more accurate than those of the traditional FEM. Moreover, the CS-FEM can provide both an upper bound and a lower bound of the strain energy solutions while using different smoothing domains.

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 to evaluate the importance of multi-input variables to multi-output responses. First, assume that a multi-input multi-output system (MIMOS) includes $n$ variables and $m$ responses. A set of summatory functions $G(x)$ and $H(x)$ are constructed by the addition and subtraction of any two response functions. Naturally, each response function is represented using a set of summatory function. Subsequently, the summatory functions $G(x)$ and $H(x)$ are further decomposed based on the high dimensional model representation (HDMR), respectively. Due to the orthogonality of all the decomposed function sub-terms, the variance and covariance of each response function can be represented using the partial variances of all the decomposed function sub-terms on the corresponding summatory functions, respectively. The total fluctuation of MIMOS is calculated by the sum of the variances and covariances on all the response functions. Further, the fluctuation is represented as the sum of the total partial variances for all the $s$-order function sub-terms, and the total partial variance is the sum of $n$ partial variances for the corresponding $s$-order function sub-terms. Then, the function sensitivity index (FSI) ${\mathrm{\text{FSI}}}_s$ for s-order function sub-terms is defined by the ratio of the total partial variance and total fluctuation, which includes first-order, second-order, and high-order FSI. The variable sensitivity index ${\mathrm{\text{VSI}}}_i$ of variable $x_i$ is calculated by the sum of all the FSIs including the contribution of variable $x_i$. Finally, numerical example and engineering application are employed to demonstrate the accuracy and practicality of the presented global sensitivity analysis method for MIMOS.

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 system of interconnected components (an effective mathematical model, a parameterizer, and an optimum search algorithm). The use of the method makes it possible to improve or provide the necessary values of the main gas-dynamic parameters of the compressor by changing the shape of the blades and their relative position. The method was tested in solving optimization problems for multistage axial compressors of gas turbine engines (the number of stages from 3 to 15). As a result, an increase in efficiency, pressure ratio, and stability margins was achieved. The presented work is a summary of a long-years investigation of the research team and aims at creating a complete picture of the obtained results for the reader. A brief description of the results of industrial compresses optimization contained in the paper is given as an illustration of the effectiveness of the developed methods.

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 region development were discussed. The analytical results were presented in a finite element model, and the effect of temperature on load–displacement curves and ultimate loads was shown based on the model. Through the nonlinear fracture mechanics, the analytical expressions of the interfacial shear stress and the load–displacement relationship can be obtained. The stress transfer mechanism, the interface crack propagation and the ductility behavior of the joints can be explained. This analytical result can help improve the potential application of fabricated structural components, precision instruments, oil and gas pipelines.

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 standard smoothed finite element method with the same triangular mesh. When using linear functions to describe strains in smoothing domains, the solutions are more accurate and stable. The contact interfaces are discretized by contact point pairs using a modified Coulomb frictional contact model. The contact problems are solved via converting into linear complementarity problems (LCPs) which can be tackled by using the Lemke method. Numerical implementations are conducted to simulate the contact behavior, including the bonding–debonding, contacting–departing and sticking–slipping. The effects of various parameters related to friction and adhesion are intensively investigated. The comparison of numerical results produced by different methods demonstrates the validity and efficiency of the NS-FEM-L for contact problems.

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 to a more accurate analysis, there has been little guidance given to the type and implementation of such an analysis. Moreover, different implementations have been adopted by various commercial software. In this paper, we discuss the use of mixed finite elements for the large deflection analysis of two-dimensional frames including shear deformation. In particular, we develop a family of elements that can be combined with different nonlinear models and discuss the effects of various assumptions and approximations that are commonly used to simplify the analysis. Examples are given to illustrate the various issues discussed.

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. This scheme is capable of coupling two numerical models with possibly dissimilar spatial discretization lengths and material properties, hence it is appealing for a multi-scale and/or multi-resolution analysis. The method developed in this paper employs an interface force–displacement coupling to yield the multi-scale model equations. It is shown that the governing equations contain a self-coupling term that affects the stability of the system, as it contributes to additional stiffness at the interface. Stability analysis is presented in terms of rotations of two vectors in $\beta$ space, where each vector represents individual model’s stability. Three model configurations of practical interest were investigated, analytical formulae derived and used to analyze stability. These analytical formulae were compared against results from numerical simulations and perfect agreement was observed.

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 to physical space through the nonsingular transformation matrices. To make the curve boundary able to be compatible well, the second-order scaling functions are applied to approximate geometric boundary. In addition, singular integral problems appearing in BSWI BEM are solved. Numerical examples verify that BSWI BEM has a desirable performance by comparing with conventional 2D BEM.