Cutoff wave numbers for energy-orthogonal eight-node quadrilateral plane-strain elements

This paper studies the propagation of plane harmonic waves in plane-strain solids discretized by the standard eight-node quadrilateral finite element. This element is formulated in energy-orthogonal form. It means that the stiffness matrix is split into basic and higher order components which are obtained from the mean and deviatoric strain fields, respectively. The major subject is to obtain reference values for the wave number that can be used as optimum cutoff wave number to properly capture a wave field. The procedure is based on the properties of the higher order elastic energy.     

Optimized meshfree methods for acoustics

When the Helmholtz equation is solved by numerical methods as, e.g., the finite element method (FEM), the solution suffers from the so-called pollution effect. The pollution is mainly caused by the dispersion, meaning that the numerical wave number disagrees with the wave number of the exact solution. This leads to inaccurate results, especially for high wave numbers. In order to obtain acceptable results also for higher wave numbers, either a high element resolution or elements of a higher order can be used. For either option the consequence is an increased computation time and memory capacity.Meshfree methods as the element free Galerkin method (EFGM) and the radial point interpolation method (RPIM) are not dispersion-free either, but it has been shown that meshfree methods are able to reduce the dispersion significantly. Both methods offer several parameters, which can be modified in order to obtain optimal results with respect to the dispersion effect. This work presents an exhaustive parameter study on both the EFGM and the RPIM. It is shown, that the methods can be significantly improved if certain parameters as, e.g., weighting functions, shape parameters, size of the influence domain, are chosen appropriately.     

A Spectral Finite Element Approach to Modeling Soft Solids Excited with High-Frequency Harmonic Loads

An approach for efficient and accurate finite element analysis of harmonically excited soft solids using high-order spectral finite elements is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial elements allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral element approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral elements for such problems. The spectral elements examined are tensor product elements (i.e. quad or brick elements) of high-order Lagrangian polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order elements on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction finite element model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing element order. However, the computationally optimal element order was found to strongly depend on the wave number.     

Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation

Discontinuous Galerkin finite element methods (DGFEM) offer certain advantages over standard continuous finite element methods when applied to the spatial discretisation of the acoustic wave equation. For instance, the mass matrix has a block diagonal structure which, used in conjunction with an explicit time stepping scheme, gives an extremely economical scheme for time domain simulation. This feature is ubiquitous and extends to other time-dependent wave problems such as Maxwell’s equations. An important consideration in computational wave propagation is the dispersive and dissipative properties of the discretisation scheme in comparison with those of the original system. We investigate these properties for two popular DGFEM schemes: the interior penalty discontinuous Galerkin finite element method applied to the second-order wave equation and a more general family of schemes applied to the corresponding first order system. We show how the analysis of the multi-dimensional case may be reduced to consideration of one-dimensional problems. We derive the dispersion error for various schemes and conjecture on the generalisation to higher order approximation in space     

Error Analysis for a Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation

Finite element methods for acoustic wave propagation problems at higher frequency result in very large matrices due to the need to resolve the wave. This problem is made worse by discontinuous Galerkin methods that typically have more degrees of freedom than similar conforming methods. However hybridizable discontinuous Galerkin methods offer an attractive alternative because degrees of freedom in each triangle can be cheaply removed from the global computation and the method reduces to solving only for degrees of freedom on the skeleton of the mesh. In this paper we derive new error estimates for a hybridizable discontinuous Galerkin scheme applied to the Helmholtz equation. We also provide extensive numerical results that probe the optimality of these results. An interesting observation is that, after eliminating the internal element degrees of freedom, the condition number of the condensed hybridized system is seen to be almost independent of the wave number.     

单片机温度控制系统中的工频干扰及抑制措施

工频谐波干扰在微机检测控制系统中是干扰最广的一种干扰成分．为了消除这种干扰，本文从理论上进行了较为详细的推导．提出了在温度检测控制系统中，采用模拟RC滤波和与电网电压信号同步的n倍采样数字均值滤波相结合．从而构成强抑制工频干扰的检测控制系统。并在实际的温度检测控制系统中获得了良好的效果。     

Analysis of unsteady compressible boundary layer flow via finite elements

This paper is concerned with the discrete formulation and numerical solution of unsteady compressible boundary layer flows using the Galerkin-finite element method. Linear interpolation functions for the velocity, density, temperature and pressure are used in the momentum equation and equations of continuity, energy and state. The coupled nonlinear finite element equations are approximated by a third order Taylor series expansion as temporal operator to integrate in time with Newton-Raphson type iterations performed until convergence within each time step. As an example, a boundary layer problem of a perfect gas behind a normal shock wave is solved. A comparison of the results with those by other method indicates a favorable agreement.     

Gaseous slip flow forced convection through ordered microcylinders

This is a theoretical study dealing with longitudinal gaseous slip flow forced convection between a periodic bunch of microcylinders arranged in regular array. The selected geometry has applications in microscale pin fin heat sinks used for cooling of microchips. The flow is considered to be hydrodynamically and thermally fully developed. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first order slip boundary conditions. The method considered is mainly analytical in which the governing equations and three of the boundary conditions are exactly satisfied. The remaining symmetry condition on the right-hand boundary of the typical element is applied to the solution through the point matching technique. The results show that both the Poiseuille number and the Nusselt number are decreasing functions of the degree of rarefaction characterized by the Knudsen number. While an increase in the blockage ratio leads to a higher Poiseuille number, the functionality of the Nusselt number on this parameter is not monotonic. At small and moderate values of the blockage ratio, the Nusselt number is higher for a higher blockage ratio, whereas the opposite may be right for higher values of this parameter. It is also observed that the angular variations of the parameters are reduced at smaller blockage ratios. Accordingly, the H1 and H2 Nusselt numbers are the same for small and moderate blockage ratios.     

A hybrid displacement plate element for bending and stability analysis

A hybrid displacement plate element is derived from a modified energy functional based on a variational principle. The higher order curvature terms which generate high energy densities are filtered out by using independent interpolation of curvatures and moments. The inter-element compatibility requirements are relaxed by including element discontinuities in the variational formulation. The accuracy of the element is shown to be excellent in both plate bending and buckling analysis.     

Semiconductor nanodevice simulation by multidomain spectral method with Chebyshev, prolate spheroidal and Laguerre basis functions

A new approach based on spectral method with efficient basis functions is proposed in the paper to simulate semiconductor nanodevice by solving the Schrödinger equation. The computational domain is partitioned at heterojunctions into a number of subdomains. The envelope functions in subdomains are expanded by various efficient basis functions and then patched by the BenDaniel-Duke boundary conditions to preserve exponential order of accuracy. Importantly, the consideration to choose the basis functions depends on the oscillatory characteristics of envelope functions. Three kinds of basis functions including prolate spheroidal wave functions, Chebyshev polynomials, and Laguerre-Gaussian functions are used according to the mathematical features in this work. In addition, the determinations of optimum values of scaling factor in Laguerre-Gaussian functions and bandwidth parameter in prolate spheroidal wave functions are also discussed in detail. Several quantum well examples are simulated to validate the effectiveness of the present scheme. The relative errors of energy levels achieve the order of 10⁻¹² requiring merely a few grid points.     

An error analysis approach for laminated composite plate finite element models

Errors in laminated composite plate finite element models occur at both the individual element level and at the discretization level. This paper shows that parasitic shear causes individual element errors and that its sources must be eliminated if numerically and physically correct results are to be provided by the finite element analysis. In addition, discretization errors occur when the behavior of the continuum is represented by a finite number of degrees of freedom. A procedure to estimate discretization errors in laminated composite plate finite element models and guide refinement, in order to achieve an acceptable level of accuracy, is developed. The error estimator built is based on the energy norm of the error in stress resultants.     

Boundary element method based on preliminary discretization

A new numerical method for solving wave diffraction problems is given. The method is based on the concept of boundary elements; i.e., the unknown values are the field values on the surface of the scatterer. An analog of a boundary element method rather than a numerical approximation of the initial (continuous) problem is constructed for an approximate statement of the problem on the discrete lattice. Although it reduces the accuracy of the method, it helps to simplify the implementation significantly since the Green functions of the problem are no longer singular. In order to ensure the solution to the diffraction problem is unique (i.e., to suppress fictitious resonances), a new method is constructed similarly to the CFIE approach developed for the classical boundary element method.     

Structure testing of wave propagation models used in identification of viscoelastic materials

In this paper, matrix perturbation theory is applied to test the structure of wave propagation models used to identify the complex modulus of a viscoelastic material. The analysis is based on a data matrix, containing the measured data from a number of independent experiments. The key observation is that if the structure of the model is correct then the unperturbed (noise-free) matrix is rank deficient of a known order. This means that the noise corrupted matrix will have a known number of singular values that diverge from zero only due to the measurement noise. A test quantity based on the distribution of these perturbed singular values is used, assuming that the signal-to-noise ratio is large and that measurement noise is white and Gaussian distributed. If the magnitudes of the smallest singular values are too large to be explained by the measurement noise only, the model is rejected. Data from two different types of experimental setups is explored; longitudinal wave propagation in a slender bar and the non-equilibrium SHPB procedure. It is shown that the model can be accepted in the first case, but should be rejected in the second.     

Empowering wave energy with control technology: Possibilities and pitfalls

With an increasing focus on climate action and energy security, an appropriate mix of renewable energy technologies is imperative. Despite having considerable global potential, wave energy has still not reached a state of maturity or economic competitiveness to have made an impact. Challenges include the high capital and operational costs associated with deployment in the harsh ocean environment, so it is imperative that the full energy harnessing capacity of wave energy devices, and arrays of devices in farms, is realised. To this end, control technology has an important role to play in maximising power capture, while ensuring that physical system constraints are respected, and control actions do not adversely affect device lifetime. Within the gamut of control technology, a variety of tools can be brought to bear on the wave energy control problem, including various control strategies (optimal, robust, nonlinear, etc.), data-based model identification, estimation, and forecasting. However, the wave energy problem displays a number of unique features which challenge the traditional application of these techniques, while also presenting a number of control ‘paradoxes’. This review articulates the important control-related characteristics of the wave energy control problem, provides a survey of currently applied control and control-related techniques, and gives some perspectives on the outstanding challenges and future possibilities. The emerging area of control co-design, which is especially relevant to the relatively immature area of wave energy system design, is also covered.     

红外反射式光学系统光机结构设计与分析

为实现红外双波段共孔径光学系统,设计出一种采用大孔径、无焦反射式光学系统,并详细介绍该系统结构.中波和长波MTF值在25线对下均大于0.3.考虑到该光学系统野外使用时复杂的运输环境,利用有限元法对简化后的卡塞格林式望远系统进行低阶振动特性和模态特性分析.通过比较2种材料的模态分析计算结果,最终选取铝合金为金属材料,保证1阶固有频率大于50 Hz,满足野外运输条件,说明该系统结构合理可行.     

A stabilized MITC element for accurate wave response in Reissner–Mindlin plates

Residual based finite element methods are developed for accurate time-harmonic wave response of the Reissner–Mindlin plate model. The methods are obtained by appending a generalized least-squares term to the mixed variational form for the finite element approximation. Through judicious selection of the design parameters inherent in the least-squares modification, this formulation provides a consistent and general framework for enhancing the wave accuracy of mixed plate elements. In this paper, the mixed interpolation technique of the well-established MITC4 element is used to develop a new mixed least-squares (MLS4) four-node quadrilateral plate element with improved wave accuracy. Complex wave number dispersion analysis is used to design optimal mesh parameters, which for a given wave angle, match both propagating and evanescent analytical wave numbers for Reissner–Mindlin plates. Numerical results demonstrates the significantly improved accuracy of the new MLS4 plate element compared to the underlying MITC4 element.     

基于DSP产生的SPWM波的谐波估计与分析

针对2000系列DSP产生的正弦脉宽调制（Sinusoidal Pulse Width Modulation,SPWM）波,使用傅里叶级数模型,提出了将改进的粒子群优化（Improved Particle Swarm Optimization,IPSO）用于各次谐波的幅值和相位的参数估计方法,着重分析了在不同的调制波频率和电压下,载波比与谐波总畸变率（Total Harmonic Distortion,THD）之间的关系,通过大量的实验,得到在一定范围的调制波频率和电压下,均能保持高次谐波较小,从而得到高质量的正弦输出。这一结论不仅对SPWM的产生起指导作用,而且对要求正弦交流电的用电设备有着降低高频损耗与节能的重要实际意义。     

Efficiency improvement of simulated annealing in optimal structural designs

Although simulated annealing (SA) is one of the easiest optimization algorithms available, the huge number of function evaluations deters its use in structural optimizations. In order to apply SA in structural optimization efficiently the number of finite element analyses (function evaluations) has to be reduced as much as possible. Two methods are proposed in this paper. One is to estimate the feasible region using linearized constraints and the SA searches proceed in the estimated feasible region. The other one makes SA search start with an area containing higher design variable values. The search area is then gradually moved toward the optimum point in the following temperatures. Using these approaches, it is hopeful that the number of finite element analyses in the infeasible region can be greatly reduced. The efficiency of SA is thus increased. Three examples show positive results by these methods.     

Construction of higher‐order curl‐conforming finite elements and its assembly

Different choices are available when constructing vector finite element bases in real coordinates. In this communication, two different designs of higher‐order curl‐conforming basis functions are introduced and explained, showing the particularities of its assembly. Tetrahedra and hexahedra are used as element shapes to assess the effect of triangular and quadrilateral faces on the two considered constructions of basis functions. A comparison of their robustness in terms of the condition number of the finite element matrices for a number of distortions is included.