Geometric nonlinear analysis of stiffened plates by the spline finite strip method

Geometric nonlinear analysis of stiffened plates is investigated by the spline finite strip method. von Karman’s nonlinear plate theory is adopted and the formulation is made in total Lagrangian coordinate system. The resulting nonlinear equations are solved by the Newton–Raphson iteration technique. To analyse plates having any arbitrary shapes, the whole plate is mapped into a square domain. The mapped domain is discretised into a number of strips. In this method, the displacement interpolation functions used are: the spline functions in the longitudinal direction of the strip and the finite element shape functions in the other direction. The stiffener is elegantly modelled so that it can be placed anywhere within the plate strip. The arbitrary orientation of the stiffener and its eccentricity are incorporated in the formulation. All these aspects have ultimately made the proposed approach a most versatile tool of analysis. Plates and stiffened plates are analysed and the results are presented along with those of other investigators for necessary comparison and discussion.     

Hybrid method of limit equilibrium and finite element internal force for analysis of arch dam stability against sliding

A hybrid method of limit equilibrium and finite element internal force for analysis of arch dam stability against sliding is presented.The finite element internal force method(FEIFM) is used to provide more accurate thrust forces acting on the faces of a slip body,and the limit equilibrium method(LEM) is employed to evaluate the factor of safety of the slip body.The method presented can deal with a slip body with large amount of geometrically complex slip faces.In addition,compared with the traditional LEM,...     

Stability and convergence of the two parameter cubic spline collocation method for delay differential equations

In this paper, we propose the cubic spline collocation method with two parameters for solving delay differential equations (DDEs). Some results of the local truncation error and the convergence of the spline collocation method are given. We also obtain some results of the linear stability and the nonlinear stability of the method for DDEs. In particular, we design an algorithm to obtain the ranges of the two parameters α,β which are necessary for the P-stability of the collocation method. Some illustrative examples successfully verify our theoretical results.     

A front-fixing finite element method for the valuation of American options with regime switching

American option problems under regime-switching model are considered in this paper. The conjectures in [H. Yang, A numerical analysis of American options with regime switching, J. Sci. Comput. 44 (2010), pp. 69–91] about the position of early exercise prices are proved, which generalize the results in [F. Yi, American put option with regime-switching volatility (finite time horizon) – Variational inequality approach, Math. Methods. Appl. Sci. 31 (2008), pp. 1461–1477] by allowing the interest rates to be different in two states. A front-fixing finite element method for the free boundary problems is proposed and implemented. Its stability is established under reasonable assumptions. Numerical results are given to examine the rate of convergence of our method and compare it with the usual finite element method.     

A hybrid analysis direct method in the calculus of variations

This paper presents a direct method for finding the solution of variational problems using a hybrid function. The properties of hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. An operational matrix of integration and the cross product of two hybrid function vectors are used to reduce a variational problem to the solution of algebraic equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.     

A convergence analysis of the Adomian decomposition method for an abstract Cauchy problem of a system of first-order nonlinear differential equations

In this article, we study some fundamental results concerning the convergence of the Adomian decomposition method (ADM) for an abstract Cauchy problem of a system of first-order nonlinear differential equations. Under certain conditions, we obtain upper estimates for the norm of solutions of this system. We also obtain results about the error estimates for the approximate solutions by the ADM and discuss their applications.     

Recent developments in the Trefftz method for finite element and boundary element applications

In 1926 E. Trefftz published a paper about a variational formulation which utilizes boundary integrals. Almost half a century later researchers became interested again in the ideas of Trefftz when the potential advantage of the Trefftz-method for an efficient use in numerical application on a computer was recognized. The concept of Trefftz can be used both for finite element and boundary element applications. A crucial ingredient of the Trefftz- method is a set of linearly independent trial functions which a priori satisfy the governing differential equations under consideration. In this paper an overview of some recent developments to construct trial functions for the Trefftz-method in a systematic manner is given. Using different types of approximation functions (singular or non-singular) we can obtain very accurate finite element and boundary element algorithms.     

An asymptotic estimate of the error of eigenvalues in the method of finite elements for the sturm-liouville problem

A scheme of the second order of accuracy for the Sturm—Liouville problem is constructed by the method of finite elements with the use of a special basic system of compact functions. The convergence of the method of finite elements is proved. An exact formula for estimating errors of eigenvalues is obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 28–36, March–Apni, 2000.     

A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients

We propose a compact split-step finite difference method to solve the nonlinear Schrödinger equations with constant and variable coefficients. This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost. This method also preserves some conservation laws. Numerical tests are presented to confirm the theoretical results for the new numerical method by using the cubic nonlinear Schrödinger equation with constant and variable coefficients and Gross-Pitaevskii equation.     

Computer Aided Tolerancing (CAT) platform for the design of assemblies under external and internal forces

Due to the stochastic nature of manufacturing processes, the functionality of mechanical assemblies is subject to variation defined by tolerances and manufacturing process characteristics. In many assemblies, functionality is also dependent on external and internal forces. Numerous Computer Aided Tolerancing (CAT) tools have been proposed that address tolerance analysis problems in complex mechanical assemblies; however current tools do not accommodate a general class of problem where the functionality of a design is fundamentally dependent on the effects of external and internal forces. This research addresses the limitation of CAT tools to accommodate assemblies under loading by developing a tolerance analysis platform which integrates CAD, CAE and statistical analysis tools using Process Integration and Design Optimisation (PIDO) software capabilities. The platform extends the capabilities of traditional CAT tools by enabling tolerance analysis of assemblies in which assembly characteristics are dependent on external and internal forces. To demonstrate the capabilities of the developed platform, examples of tolerance analysis problems involving external forces (compliance) and internal forces (multi-body dynamics) are presented.     

A comparison of some model order reduction methods for fast simulation of soft tissue response using the point collocation-based method of finite spheres

In this paper we develop the point collocation-based method of finite spheres (PCMFS) to simulate the viscoelastic response of soft biological tissues and evaluate the effectiveness of model order reduction methods such as modal truncation (MT), Hankel optimal model and truncated balanced realization (TBR) techniques for PCMFS. The PCMFS is a physics-based meshfree numerical technique for real time simulation of surgical procedures. Since computational speed has a significant role in simulation of surgical procedures, model order reduction methods have been compared for relative gains in efficiency and computational accuracy. Of these methods, TBR results in the highest accuracy with an average error which is within 3.37% of the full model while MT results in the highest efficiency with a computational cost reduction of 54.2% compared to the full model.     

Entropy generation analysis and heatline visualization of free convection in nanofluid (KKL model-based)-filled cavity including internal active fins using lattice Boltzmann method

Two-dimensional natural convection and entropy generation in a square cavity filled with CuO–water nanofluid is performed. The lattice Boltzmann method is employed to solve the problem numerically. The influences of different Rayleigh numbers $\left(10^3<Ra<10^6\right)$ and solid volume fractions $\left(0<\phi <0.05\right)$ on the fluid flow, heat transfer and total/local entropy generation are presented comprehensively. Also, the heatline visualization is employed to identify the heat energy flow. To predict the thermo-physical properties, dynamic viscosity and thermal conductivity, of CuO–water nanofluid, the KKL model is applied to consider the effect of Brownian motion on nanofluid properties. It is concluded that the configurations of active fins have pronounced effect on the fluid flow, heat transfer and entropy generation. Furthermore, the Nusselt number has direct relationship with Rayleigh number and solid volume fraction, and the entropy generation has direct and reverse relationships with Rayleigh number and solid volume fraction, respectively.     

A mortar spectral method for the analysis and optimization of L-shaped laminated plates

We present a new mortar approach in the spectral context for the analysis and optimization of L-shaped thin composite laminates. Its roots may be found in the (very few) existing mortar approaches for the bi-Laplacian that are herein extended to handle the fourth-order elliptic operator governing thin anisotropic laminates. For the computation of the structural matrices, exact symbolic integration is used rather than more classical Gauss–Lobatto quadrature schemes. Thanks to the underlying spectral approach, considerable CPU times savings are obtained compared with finite-element approaches when the optimal design of the laminates is pursued. A few numerical studies that are concerned with the analysis and the optimization of L-shaped single-layered plates are described in detail.     

CAVE: A package for detection and quantitative analysis of internal cavities in a system of overlapping balls: Application to proteins

We developed a software package (CAVE) in Fortran language to detect internal cavities in proteins which can be applied also to an arbitrary system of balls. The volume, the surface area and other quantitative characteristics of the cavities can be calculated. The code is based on the recently suggested enveloping triangulation algorithm [J. Buša et al., J. Comp. Chem. 30 (2009) 346] for computing volume and surface area of the cavity by analytical equations. Different standard sets of atomic radii can be used. The PDB compatible file containing the atomic coordinates must be stored on the disk in advance. Testing of the code on different proteins and artificial ball systems showed efficiency and accuracy of the algorithm. The program is fast. It can handle a system of several thousands of balls in the order of seconds on contemporary PC's. The code is open source and free.

Program summary

Program title: CAVECatalogue identifier: AEHC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHC_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 8670No. of bytes in distributed program, including test data, etc.: 100 131Distribution format: tar.gzProgramming language: FortranComputer: PC Pentium and CoreOperating system: Linux system and Windows XP systemClassification: 16.1Nature of problem: Molecular structure analysis.Solution method: Analytical method for cavities detection, and numerical algorithm for volume and surface area calculation based on the analytical formulas, after using the stereographic transformation.Running time: Depends on the size of the molecule under consideration. The test example included in the distribution takes about 1 minute to run.     

A stencil of the finite-difference method for the 2D convection diffusion equation and its new iterative scheme

The paper gives the numerical stencil for the two-dimensional convection diffusion equation and the technique of elimination, and builds up the new iterative scheme to solve the implicit difference equation. The scheme's convergence and its higher rate of convergence than the Jacobi iteration are proved. And the numerical example indicates that the new scheme has the same parallelism and a higher rate of convergence than the Jacobi iteration.     

Hybrid method of analysis of slot discontinuity in a rectangular waveguide and the validity of circuit representation

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide (also called edge slot) is presented. The slot aperture field is expanded in terms of entire domain sinusoidal basis functions and is solved using Galerkin's method. The computed results have been compared with the measured data published in the previous literature to validate the present analysis. The validity of representing the edge slot as a shunt element is examined and an alternate way of representing the edge slot is suggested as being more accurate. © 1998 John Wiley & Sons, Inc. Int J RF and Microwave CAE 8: 339–349, 1998.     

Extended finite element method (XFEM) analysis of fiber reinforced composites for prediction of micro-crack propagation and delaminations in progressive damage: a review

Microsystem Technologies - Various methodologies and frameworks have been developed for extended finite element method (XFEM) to simulate two-dimensional and three-dimensional microcrack initiation...     

A simple,accurate method to compute brightness temperature and/or radiance for the thermal infrared channels of the Advanced Very High Resolution Radiometer (AVHRR)

Users of thermal infrared data from the AVHRR on a NOAA polar-orbiting operational satellite convert the count value output to radiance units, and then assign an equivalent blackbody temperature to the radiance value. Assigning a blackbody temperature to the radiance value is an indirect process, which requires knowledge of the AVHRR spectral response function and a fairly complex calculation. Both difficulties can be avoided by the simple two-step process shown in this Letter. First, blackbody temperature is estimated from a square-root of the measured radiance, then the estimate is refined by values from a ‘universal’ correction curve. The RMS difference between this approximation and the complex calculation is a few hundredths deg K for temperatures in the 200-320 deg K range. The inverse computation, radiance from temperature, is accurate to within 0·01-0·02mWm^?2sr^?1 (cm^?1)^?1. Results are shown for the NOAA-7, -9, -11, and -12 spacecraft.     

A new ZK-ILW equation for algebraic gravity solitary waves in finite depth stratified atmosphere and the research of squall lines formation mechanism

The research of algebraic gravity solitary waves is an advanced field which has important practical and theoretical value in physical, oceanography, aerology and etc. By calculation condition and theoretical method limit, previous researches mainly focused on the $(1+1)$ dimensional models, and $(2+1)$ dimensional models were few considered. In this paper, from the non-static equilibrium equation, a new ZK-ILW equation is derived by using multi-scale analysis and perturbation method in finite depth stratified atmosphere, which is the first time obtained. The model can reduce to ZK-BO model $(h\to \infty )$, and ZK model $(h\to 0)$ and is the generalization of the above two models. In order to further understand the nature of algebraic gravity solitary waves, we get the analytical solution of ZK-ILW equation by using the trial function method and discuss the conservation laws. Furthermore, the fission process of algebraic gravity solitary waves is studied, and we can judge that one of the possible formation mechanism of squall lines is the fission of algebraic gravity solitary waves.     

A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations

In this study, the decomposition method for solving the linear heat equation and nonlinear Burgers equation is implemented with appropriate initial conditions. The application of the method demonstrated that the partial solution in the x-direction requires more computational work when compared with the partial solution developed in the t-direction but the numerical solution in the x-direction are performed extremely well in terms of accuracy and efficiency.