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1 – 10 of 407Chein-Shan Liu and Jiang-Ren Chang
The purpose of this paper is to solve the second-order nonlinear boundary value problem with nonlinear boundary conditions by an iterative numerical method.
Abstract
Purpose
The purpose of this paper is to solve the second-order nonlinear boundary value problem with nonlinear boundary conditions by an iterative numerical method.
Design/methodology/approach
The authors introduce eigenfunctions as test functions, such that a weak-form integral equation is derived. By expanding the numerical solution in terms of the weighted eigenfunctions and using the orthogonality of eigenfunctions with respect to a weight function, and together with the non-separated/mixed boundary conditions, one can obtain the closed-form expansion coefficients with the aid of Drazin inversion formula.
Findings
When the authors develop the iterative algorithm, removing the time-varying terms as well as the nonlinear terms to the right-hand sides, to solve the nonlinear boundary value problem, it is convergent very fast and also provides very accurate numerical solutions.
Research limitations/implications
Basically, the authors’ strategy for the iterative numerical algorithm is putting the time-varying terms as well as the nonlinear terms on the right-hand sides.
Practical implications
Starting from an initial guess with zero value, the authors used the closed-form formula to quickly generate the new solution, until the convergence is satisfied.
Originality/value
Through the tests by six numerical experiments, the authors have demonstrated that the proposed iterative algorithm is applicable to the highly complex nonlinear boundary value problems with nonlinear boundary conditions. Because the coefficient matrix is set up outside the iterative loop, and due to the property of closed-form expansion coefficients, the presented iterative algorithm is very time saving and converges very fast.
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The purpose of this paper is to consider divergence of composite plate wings as well as slender wings with thin-walled cross-section of small-size airplanes. The main attention is…
Abstract
Purpose
The purpose of this paper is to consider divergence of composite plate wings as well as slender wings with thin-walled cross-section of small-size airplanes. The main attention is paid to establishing of closed-form mathematical solutions for models of wings with coupling effects. Simplified solutions for calculating the divergence speed of wings with different geometry are established.
Design/methodology/approach
The wings are modeled as anisotropic plate elements and thin-walled beams with closed cross-section. Two-dimensional plate-like models are applied to analysis and design problems for wings of large aspect ratio.
Findings
At first, the equations of elastic deformation for anisotropic slender, plate-like wing with the large aspect ratio are studied. The principal consideration is delivered to the coupled torsion-bending effects. The influence of anisotropic tailoring on the critical divergence speed of the wing is examined in closed form. At second, the method is extended to study the behavior of the large aspect ratio, anisotropic wing with box-like wings. The static equations of the wing with box-like profile are derived using the theory of anisotropic thin-walled beams with closed cross-section. The solutions for forward-swept wing with box-like profiles are given in analytical formulas. The formulas for critical divergence speed demonstrate the dependency upon cross-sectional shape characteristics and anisotropic properties of the wing.
Research limitations/implications
The following simplifications are used: the simplified aerodynamic theory for the wings of large aspect ratio was applied; the static aeroelastic instability is considered (divergence); according to standard component methodology, only the component of wing was modeled, but not the whole aircraft; the simplified theories (plate-lime model for flat section or thin-walled beam of closed-section) were applied; and a single parameter that defines the rotation of a stack of single layers over the face of the wing.
Practical implications
The simple, closed-form formulas for an estimation of critical static divergence are derived. The formulas are intended for use in designing of sport aircraft, gliders and small unmanned aircraft (drones). No complex analysis of airflow and advanced structural and aerodynamic models is necessary. The expression for chord length over the span of the wing allows for accounting a board class of wing shapes.
Social implications
The derived theory facilitates the use of composite materials for popular small-size aircraft, and particularly, for drones and gliders.
Originality/value
The closed-form solutions for thin-walled beams in steady gas flow are delivered in closed form. The explicit formulas for slender wings with variable chord and stiffness along the wing span are derived.
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Tarikul Islam and Armina Akter
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to…
Abstract
Purpose
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional
Design/methodology/approach
The rational fractional
Findings
Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.
Originality/value
The rational fractional
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The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length…
Abstract
Purpose
The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length and withstand tension and bending. The constitutive equations of the lattice in discrete and differential formulations are derived. Two complementary systems of loads, which cause different deformation two orthogonal families of fibers, occur in the lattice. The fracture behavior of the material containing a semi-infinite crack is investigated. The crack problem reduces to the exactly solvable Riemann-Hilbert problem. The solution demonstrates that the behavior of material cardinally depends upon the tension in the orthogonal family of fibers. If tension in fibers exists, opening of the crack under action of loads in two-dimensional lattice is similar to those in elastic solid. In the absence of tension, contrarily, there is a finite angle between edges at the crack tip.
Design/methodology/approach
The description of stress state in the crack vicinity is reduced to the solution of mixed boundary value problem for simultaneous difference equations. In terms of Fourier images for unknown functions the problem is equivalent to a certain Riemann-Hilbert problem.
Findings
The analytical solution of the problem shows that fracture behavior of the material depends upon the presence of stabilizing tension in fibers, parallel to crack direction. In the presence of tension in parallel fibers fracture character of two-dimensional lattice is similar to behavior of elastic solid. In this case the condition of crack grows can be formulated in terms of critical stress intensity factor. Otherwise, in the absence of stabilizing tension, the crack surfaces form a finite angle at the tip.
Research limitations/implications
Linear behavior of fibers until rupture. Small deflections. Perfect two-dimensional lattice.
Practical implications
The model provides exact analytical estimation of stresses on the crack tip as the function of fibers’ stiffness.
Originality/value
The model is the extension of known lattice models, taking into account the semi-infinite crack in the lattice. This is the first known closed form solution for an infinite lattice model with the crack.
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Fathi Jegarkandi Mohsen, Salezadeh Nobari Ali, Sabzehparvar Mahdi, Haddadpour Hassan and Tavakkoli Farhad
The purpose of this paper is to investigate the aeroelastic behavior of a supersonic flight vehicle flying at moderate angles of attack using global analytic nonlinear aerodynamic…
Abstract
Purpose
The purpose of this paper is to investigate the aeroelastic behavior of a supersonic flight vehicle flying at moderate angles of attack using global analytic nonlinear aerodynamic model.
Design/methodology/approach
Aeroelastic behavior of a supersonic flight vehicle flying at moderate angles of attack is considered, using nonlinear aerodynamics and linear elastodynamics and structural models. Normal force distribution coefficient over the length of the vehicle and pitching moment coefficient are the main aerodynamic parameters used in the aeroelastic modeling. It is very important to have closed form analytical relations for these coefficients in the model. They are generated using global nonlinear multivariate orthogonal modeling functions in this work. Angle of attack and length of the vehicle are selected as independent variables in the first step. Local variation of angle of attack is applied to the analytical model and due to its variation along the body of the vehicle, equations of motion are finalized. Mach number is added to the independent variables to investigate its role on instability of the vehicle and the modified model is compared with the previous one in the next step. Thrust effect on the aeroelastic stability of the vehicle is analyzed at final stage.
Findings
It is shown that for the vehicles having simple configurations and low length to diameter ratios flying at low angles of attack, assuming normal force distribution coefficient linear relative to α is reasonable. It is concluded that vehicle's velocity and thrust has not great effect on its divergence dynamic pressure.
Originality/value
Based on the constructed model, a simulation code is generated to investigate the aeroelastic behavior of the vehicle. The resultant code is verified by investigating the static aeroelastic stability margin of the vehicle presented in the references. Mach number effect on the aeroelastic behavior of the vehicle is considered using modified aerodynamic model and is compared with the results. Data base for identifying aerodynamic coefficients is conducted using CFD code.
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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community…
Abstract
Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.
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Frédérique Le Louër and María-Luisa Rapún
In this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional…
Abstract
Purpose
In this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.
Design/methodology/approach
From the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.
Findings
As the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.
Originality/value
The authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.
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Alex Paseka and Aerambamoorthy Thavaneswaran
Recently, Stein et al. (2016) studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE)…
Abstract
Purpose
Recently, Stein et al. (2016) studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE). In this paper, the authors extend the model to a wider class of memory kernels and then propose a bond and bond option valuation model based on the extension of the generalized Langevin process of Stein et al. (2016).
Design/methodology/approach
Bond and bond option pricing based on the proposed interest rate models presents new difficulties as the standard partial differential equation method of stochastic calculus for bond pricing cannot be used directly. The authors obtain bond and bond option prices by finding the closed form expression of the conditional characteristic function of the integrated short rate process driven by a general Lévy noise.
Findings
The authors obtain zero-coupon default-free bond and bond option prices for short rate models driven by a variety of Lévy processes, which include Vasicek model and the short rate model obtained by solving a second-order Langevin stochastic differential equation (SDE) as special cases.
Originality/value
Bond and bond option pricing plays an important role in capital markets and risk management. In this paper, the authors derive closed form expressions for bond and bond option prices for a wider class of interest rate models including second-order SDE models. Closed form expressions may be especially instrumental in facilitating parameter estimation in these models.
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Zhihua Niu, Zhimin Li, Sun Jin and Tao Liu
This paper aims to carry out assembly variation analysis for mechanisms with compliant joints by considering deformations induced by manufactured deviations. Such an analysis…
Abstract
Purpose
This paper aims to carry out assembly variation analysis for mechanisms with compliant joints by considering deformations induced by manufactured deviations. Such an analysis procedure extends the application area of direct linearization method (DLM) to compliant mechanisms and also illustrates the dimensional interaction within multi-loop compliant structures.
Design/methodology/approach
By applying DLM to both geometrical equations and Lagrange’s equations of the second kind, an analytical deviation modeling method for mechanisms with compliant joints are proposed and further used for statistical assembly variation analysis. The precision of this method is verified by comparing it with finite element simulation and traditional DLM.
Findings
A new modeling method is proposed to represent kinematic relationships between joint deformations and parts/components deviations. Based on a case evaluation, the computational efficiency is improved greatly while the modeling accuracy is maintained at more than 94% rate comparing with the benchmark finite element simulation.
Originality/value
The Equilibrium Equations of Incremental Forces derived from Lagrange’s equations are proposed to quantitatively represent the relationships between manufactured deviations and assembly deformations. The present method extends the application area of DLM to compliant structures, such as automobile suspension systems and some Micro-Electro-Mechanical-Systems.
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JIAKANG ZHONG, LOUIS C. CHOW and WON SOON CHANG
An eigenvalue method is presented for solving the transient heat conduction problem with time‐dependent or time‐independent boundary conditions. The spatial domain is divided into…
Abstract
An eigenvalue method is presented for solving the transient heat conduction problem with time‐dependent or time‐independent boundary conditions. The spatial domain is divided into finite elements and at each finite element node, a closed‐form expression for the temperature as a function of time can be obtained. Three test problems which have exact solutions were solved in order to examine the merits of the eigenvalue method. It was found that this method yields accurate results even with a coarse mesh. It provides exact solution in the time domain and therefore has none of the time‐step restrictions of the conventional numerical techniques. The temperature field at any given time can be obtained directly from the initial condition and no time‐marching is necessary. For problems where the steady‐state solution is known, only a few dominant eigenvalues and their corresponding eigenvectors need to be computed. These features lead to great savings in computation time, especially for problems with long time duration. Furthermore, the availability of the closed form expressions for the temperature field makes the present method very attractive for coupled problems such as solid—fluid and thermal—structure interactions.
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