International Journal of Computational Methods

This paper is devoted to the interval identification of structural parameters in the aspect of uncertainty propagation and uncertainty quantification. The accurate interval estimation of structural responses can be efficiently obtained by application of Monte Carlo (MC) simulation combined with surrogate models. By means of the concept of interval length, a novel quantitative metric named as interval deviation degree (IDD) is constructed to characterize the disagreement of interval distributions between analytical modal data and measured modal data. The nominal values and interval radii of the system parameters are well estimated by solving two optimization problems. Finally, numerical and experimental case studies are given to illustrate the feasibility of the proposed method in the interval identification of structural parameters.

In this paper, a digital-image-driven stochastic homogenization method is developed to analyze elastic heterogeneous media such as recycled aggregate concrete (RAC), etc. This linking can be accomplished in an efficient manner by exploiting the excellent synergy of finite pixel-element method and Monte Carlo simulation for the computation of the effective properties of the random five-phase composite. The pixel-point discretization of system geometry is used for the approximation of the mechanical response of the elastic heterogeneous microstructure. Using nanoindentation technique and scanning electron microscopy, tens of digital images of modulus map of the five-phase heterogeneous material are made. Using the moving window technique and the Monte Carlo method, the random elastic moduli of the five phases at micro-scale are obtained. Then the effective elastic modulus of the meso-scale representative volume element (RVE) is computed based on spectral stochastic finite element method. Finally, the effective modulus is used to analyze the global behavior of RVE at macro-scale. Then the finite pixel-element method is used to investigate the effect of microscopic covariance noise on the global material properties, as well as the computational efficiency. The results show that the digital image method is an accurate and efficient tool to investigate the random material properties across scales.

This paper develops an uncertainty propagation analysis method to analyze transmit/receive (T/R) modules with uncertain parameters, such as variability and tolerances in the physical parameters and geometry produced in the manufacturing processes. The method is a combination of the variance decomposition-based sensitivity analysis and the moment-based arbitrary polynomial chaos (MBaPC). First, the electromagnetic simulation model of a practical T/R module is created. Secondly, based on the model, the sensitivity analysis is carried out to determine the sensitive parameters to the amplitude difference and the phase difference between the input and output electromagnetic signal. Thirdly, their four order statistical moments are calculated using the MBaPC. At last, according to the maximum entropy principle, the statistical moments are used to fit the probability distribution functions of the amplitude difference and the phase difference of the T/R module. The results computed by MBaPC have been validated accurate and efficient compared with Monte Carlo simulation approach.

This work presents multiphysics numerical analysis of piezoelectric actuators realized using the finite element method (FEM) and their performances to analyze the structure-electric interaction in three-dimensional (3D) piezoelectric continua. Here, we choose the piezoelectric bimorph actuator without the metal shim and with the metal shim as low-frequency problems and a surface acoustic wave device as a high-frequency problem. More attention is given to low-frequency problems because in our application micro air vehicle’s wings are actuated by piezoelectric bimorph actuators at low frequency. We employed the Newmark’s time integration and the central difference time integration to study the dynamic response of piezoelectric actuators. Monolithic coupling, noniterative partitioned coupling and partitioned iterative coupling schemes are presented. In partitioned iterative coupling schemes, the block Jacobi and the block Gauss–Seidel methods are employed. Resonance characteristics are very important in micro-electro-mechanical system (MEMS) applications. Therefore, using our proposed coupled algorithms, the resonance characteristics of bimorph actuator is analyzed. Comparison of the accuracy and computational efficiency of the proposed numerical finite element coupled algorithms have been carried out for 3D structure–electric interaction problems of a piezoelectric actuator. The numerical results obtained by the proposed algorithms are in good agreement with the theoretical solutions.

To improve the precision in resolving interfacial crack intensity factor of piezoelectric bimaterials in practical engineering, we proposed a cell-based smoothed finite element method (CS-FEM) that simulated the displacement field and electric field near the crack tips of piezoelectric bimaterials. The displacement field and electric field at the nodes behind crack tips were extracted and substituted into the extrapolation method of interfacial cracks of out-of-phase anisotropic piezoelectric bimaterials, aiming to solve the interfacial crack intensity factor of transversally isotropic piezoelectric bimaterials. With double-piezoelectric flat-plates containing center cracks as example, we investigated the intensity factors of different materials, loads, cell number and encryption modes. The results were compared with FEM and analytic solutions. Results of numerical cases showed that CS-FEM was computationally simple, precise and reliable and thus was attractive to engineers.

A step length adjustment (SLA) iterative algorithm was proposed for locating the minimum performance target point (MPTP) in the inverse reliability analysis. This paper elaborates SLA and two deliberately designed numerical examples are used to compare SLA with other algorithms appearing in recent literatures for locating MPTP. The results show that SLA is much more robust and efficient. Then SLA and sequential optimization and reliability assessment (SORA) are combined to solve reliability-based design optimization (RBDO) problems. In the reliability assessment of SORA, with the design obtained from the previous cycle, SLA is used to locate MPTP. Then in the deterministic optimization, the boundaries of violated constraints are shifted to the feasible direction according to the MPTP obtained in the reliability assessment. Several examples frequently cited in similar studies are used to compare SORA-SLA with other RBDO algorithms. The results indicate the effectiveness and robustness of SORA-SLA.

The identification of multivalued parameters is formulated as a constraint minimization problem called primal problem. We embed it in a family of perturbed problems and we associate a dual problem with it using the conjugate functions. Basing on the primal-dual relationship, under some qualification conditions on the parameters to be identified we elaborate the well posedeness, convergence and stability of the solution assuming. Numerical simulations are described in the end for the identification of discontinuous dispersion tensor in transport equations.

A new family of noniterative algorithms with controllable numerical dissipations for structural dynamics is studied. Particularly, this paper provides nine members of the proposed algorithms and two existing methods are included as two special cases. The proposed algorithms achieve unconditional stability and are second-order accurate for linear elastic systems. The explicit expressions of stability conditions for nonlinear stiffness systems are completely presented, which shows that new algorithms possess unconditional and conditional stability for stiffness softening and hardening systems, respectively. A comprehensive stability and accuracy analysis, including numerical energy dissipations and dispersions, are studied in order to gain insight into spectral properties of new algorithms. Due to the existence of the nonzero spurious root, this paper also pays attention to the influence of the spurious root, which shows that the spurious root does not influence numerical accuracy at low-frequency domains. Although the proposed algorithms exhibit the unusual overshoot behaviors in either displacement or velocity, numerical damping ratios in new algorithms can significantly eliminate this overshoot at a few steps. The new dissipative algorithms are appropriate to solve numerical transient responses of the structure. Numerical examples are also presented to demonstrate the analytical results.

Atherosclerosis, which is commonly seen at regions with low wall shear stress (WSS) level in bifurcations, is a kind of fibro-fatty plaque accumulated on arterial walls. Aortic and iliac bifurcations have the highest proportion of patients among all atherosclerosis cases, thus it is necessary to numerically analyze the flow distribution and predict plaque positions in these bifurcations. Furthermore, using fluid–solid interaction (FSI) method could obtain a more exact flow pattern in arteries. In this study, a patient-specific model of aortic and iliac bifurcations was simulated with both FSI and rigid-wall cases. We analyzed the vessel deformation, WSS and flow distribution of this model. Computed tomography (CT) angiography was used in our study to create patient-specific model of aorto-iliac arteries. Real material properties and pulsatile fluid boundary conditions were applied in solid and fluid zones, respectively. We performed FSI and ordinary computational fluid dynamics (CFD) simulations with AYSYS 15.0 software (ANSYS Inc., Canonsburg, PA), and compared the diameter change, WSS and flow field between these two results. The diameter change between systolic phase and diastolic phase is 8–9% on abdominal aorta, and 3% on external and internal iliac arteries. The compliance of vessels corresponds to in-vivo observations. At peak systolic phase, the average WSS obtained in FSI simulation is 10% lower than in rigid-wall result, area of low-WSS region ($\mathrm{\text{WSS}}\le 0.5\mathrm{\text{Pa}}$) also increases by 78%. Wall deformation has a greater impact on WSS of those vessels with larger diameter, but hardly changes the shear level in smaller branches. Our result also shows that iliac bifurcations reveal more complicated secondary flow in systolic phase, comparing to other vessels, and stenosed iliac artery has more severe secondary flow than healthy artery. We obtained a feasible method for hemodynamic FSI research. The material parameters, boundary conditions and mesh could be used for further simulations, while the WSS and flow distribution may support clinical diagnosis and treatment. We concluded that compliance is a must-consider factor for simulating an accurate wall shear stress, because the vessel deformation in FSI simulation will significantly change the distribution of low-WSS zones. Moreover, more complicated secondary flow is detected in iliac arteries because it may interact between bifurcations. Stenosis in artery may also have a blocking effect on downstream blood flow.

This paper presents discontinuous Legendre wavelet element (DLWE) approach for solving nonlinear reaction–diffusion equation (RDE) arising in mathematical chemistry. Firstly, weak formulation of the RDE and corresponding numerical fluxes are devised by utilizing the advantages of both Legendre wavelet and discontinuous Galerkin (DG) approach. Secondly, stability and error estimates of the proposed method have been addressed. Finally, numerical experiments demonstrate the validity and utility of the DLWE method, which is also applicable to solving some other kinds of partial differential equations.

In this paper, we developed a GPU parallelized Total Lagrangian Formation of Smoothed Particle Hydrodynamics (TLSPH) algorithm for 3D geometrical nonlinear structure analysis. The code was developed using NVDIA CUDA C++. Both the TLSPH and GPU parallelization algorithms are described in detail. Compared to the traditional FEM method for structure analysis, TLSPH method is much easier to be implemented and parallelized. In addition, as a meshless based method, there is no need to mesh the domain for TLSPH method. Also, the computational cost of TLSPH is much lower than the Weakly Compressible Smoothed Particle (WCSPH) method. By introducing GPU acceleration, we have significantly improved the code performance. Two benchmark test cases for 3D geometrical nonlinear structure analysis are carried out. The simulation results are compared with analysis results and the data obtained by Abaqus, which is a popularly-used software for structure analysis based on FEM method. In order to show the efficiency of GPU parallelization, a serial code based on the same TLSPH method is also developed as a reference. Results show GPU parallelization accelerates the code obviously. In summary, the GPU parallelized TLSPH method shows the potential to become an alternative way to deal with 3D geometrical nonlinear structure analysis.

In many real life applications, the behavior of the system is modeled by a boundary value problem (BVP) for a linear differential equation. If the uncertainties in the boundary values, the right-hand side function and the coefficient functions are to be taken into account, then in many cases an interval boundary value problem (IBVP) arises. In this study, for such an IBVP, we propose a different approach than the ones in common use. In the investigated IBVP, the boundary values are intervals. In addition, we model the right-hand side and coefficient functions as bunches of real functions. Then, we seek the solution of the problem as a bunch of functions. We interpret the IBVP as a set of classical BVPs. Such a classical BVP is constructed by taking a real number from each boundary interval, and a real function from each bunch. We define the bunch consisting of the solutions of all the classical BVPs to be the solution of the IBVP. In this context, we develop a numerical method to obtain the solution. We reduce the complexity of the method from $O(n^5)$ to $O(n^2)$ through our analysis. We demonstrate the effectiveness of the proposed approach and the numerical method by test examples.

When mentioning multidisciplinary design optimization methods, the deterministic optimum design is frequently applied to set the constraint boundary. Furthermore, only a small amount of space tolerances (or uncertainty) is available in the process of design, manufacture and operation. Therefore, deterministic optimum design lacking uncertainty cannot meet the needs of reliability-based design optimization. In this paper, reliability optimization design method, finite element (FE) analysis, optimal Latin hypercube test design and response surface approximation model are combined to optimize the side structure of electric vehicles and improve its crashworthiness. Firstly, a side impact FE model of the electric vehicle is established and verified in this paper. Then, the dimensions and the material yield strength of the force-bearing structure in the vehicle are selected as design variables, and the impact speed in the actual collision is selected as a random variable to optimize the car crashworthiness in the side impact using the 95% reliability optimization method. The results show that the 95% reliability optimization design increases the total energy absorption of the side components by 9.45%, the intrusion of the B-pillar and the vehicle door inner panel decreased by 10.42% and 14.75%, respectively. The intrusion speed of the B-pillar and the inner panel of the vehicle door decreases by 10.35% and 17.78%, respectively. By comparing the results of traditional deterministic optimization and reliability optimization methods, the latter can better satisfy the crash safety objectives, and improve the reliability of vehicle body design.

An out-of-core block Lanczos method with the OpenMP parallel scheme was developed to solve large spare damped eigenproblems. The symmetric generalized eigenproblem is first solved using the block Lanczos method with the preconditioned conjugate gradient (PCG) method, and the condensed damped eigenproblem is then solved to obtain the complex eigenvalues. Since the PCG solvers and out-of-core schemes are used, a large-scale eigenproblem can be solved using minimal computer memory. The out-of-core arrays only need to be read once in each Lanczos iteration, so the proposed method requires little extra CPU time. In addition, the second-level OpenMP parallel computation in the PCG solver is suggested to avoid using a large block size that often increases the number of iterations needed to achieve convergence.