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The objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.

The porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.

The direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.

Analytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

This paper aims to develop an efficient surface‐plane intersection (SPI) algorithm for direct slicing of free‐form surfaces to be produced by layered manufacturing.

A semi‐analytical method for direct slicing has been formulated and tested on Bezier and B‐spline surfaces commonly used in CAD modeling. This method solves for the intersection points by a “root” finding procedure and establishes their connectivity, unlike the conventional “marching” procedures.

The proposed algorithm solves intersection contours between free form surfaces and planes. The solution procedure is efficient with respect to computational time and accuracy (feature detection) over some of the conventional SPI strategies. The method involves a global solution procedure in contention with the traditional methodologies which are generally spatially distinctive in approach.

Use of higher order terms in the representation of parametric surfaces makes the algorithm computationally intensive and time‐expensive.

This algorithm would be of practical use in the direct slicing of free form surfaces used in CAD modeling. Direct slicing methods solve for the actual intersection of surface and plane without resorting to “tessellation.” Reducing the computation time and detection of features within a given resolution is of primary importance for developing commercial rapid prototyping software, which is achieved in the present paper.

A novel method has been developed for SPI for use in direct slicing of CAD models. While a major proportion of the direct slicing strategies employ the “marching” procedure involving determination of “critical points,” the proposed method utilizes the evaluation of “roots” of a surface in a global manner to determine the intersection points with proper connectivity. Hence, it is effective in reducing the computation time and is simple but generic in approach. Although Bezier and B‐spline surfaces are used as the representative cases, the algorithm can be extended for any parametric surface for direct slicing.

The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study.

A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme.

The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study.

The obtained results are new and presented for the first time in the literature.

This paper aims to present harmonic response of magneto‐electro‐elastic cylinder by quasi‐static and fully dynamic electromagnetic theories. The quasi‐static assumption uses magnetic scalar potential whereas magnetic vector potential is employed in a fully dynamic model.

The electric field induced by time varying magnetic field is non‐conservative and can be described by electric scalar potential and magnetic vector potentials.

The magnitude of vector potential is dominant in axial and circumferential direction whereas the magnetic flux density is significant in radial direction. Magnetic scalar potential approach evaluates only the radial component of magnetic flux density and electric field intensity is reasonably the same as that of the magnetic vector potential approach.

Semi‐analytical finite element method is used in this paper and the vector potential is formulated in cylindrical coordinates.

The purpose of this study, which is designed for the implementation of models in the implicit finite element framework, is to propose a robust, stable and efficient explicit integration algorithm for rate-independent elasto-plastic constitutive models.

The proposed automatic substepping algorithm is founded on an explicit integration scheme. The estimation of the maximal subincrement size is based on the stability analysis.

In contrast to other explicit substepping schemes, the algorithm is self-correcting by definition and generates no cumulative drift. Although the integration proceeds with maximal possible subincrements, high level of accuracy is attained. Algorithmic tangent stiffness is calculated in explicit form and optionally no analytical second-order derivatives are needed.

The algorithm is convenient for elasto-plastic constitutive models, described with an algebraic constraint and a set of differential equations. This covers a large family of materials in the field of metal plasticity, damage mechanics, etc. However, it cannot be directly used for a general material model, because the presented algorithm is convenient for solving a set of equations of a particular type.

The estimation of the maximal stable subincrement size is computationally cheap. All expressions in the algorithm are in explicit form, thus the implementation is simple and straightforward. The overall performance of the approach (i.e. accuracy, time consumption) is fully comparable with a default (built-in) ABAQUS/Standard algorithm.

The estimated maximal subincrement size enables the algorithm to be stable by definition. Subincrements are much larger than those in conventional substepping algorithms. No error control, error correction or local iterations are required even in the case of large increments.

To provide a new semi‐analytical procedure which is much faster than FEM and for this reason can be applied in a reconstruction of an interface between two conducting fluids (magnetic fluid dynamics problem) by means of magnetic field tomography.

Three approaches are compared: a simple analytical solution (AS1), a modified semi‐analytical solution (AS2), and the finite element method solution. The modified semi‐analytical approach takes into account an information about azimuthal spatial harmonics received from the Fourier analysis of magnetic flux density distributions calculated by FEM. AS1 and AS2 have been compared for different modes of the interface using FEM solution as a reference.

It is shown that for small perturbations the AS2 in every case provides smaller errors than AS1 although for some modes (14,24) the quality of the solution is still not satisfactory.

This paper describes a new technique for the analysis of electromagnetic field which can be also applied in other problems.

Recently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique for the solution of these types of differential equations, as sometimes it is not easy to get the analytical solution. However, in general, in the existing investigations, involved parameters and variables are defined exactly, whereas in actual practice it may contain uncertainty because of error in observations, maintenance induced error, etc. Therefore, the purpose of this paper is to find the dynamic response of fractionally damped beam approximately under fuzzy and interval uncertainty.

Here, a semi analytical approach, variational iteration method (VIM), has been considered for the solution. A newly developed form of fuzzy numbers known as double parametric form has been applied to model the uncertainty involved in the system parameters and variables.

VIM has been successfully implemented along with double parametric form of fuzzy number to find the uncertain dynamic responses of the fractionally damped beam. The advantage of this approach is that the solution can be written in power series or compact form. Also, this method converges rapidly to have the accurate solution. The uncertain responses subject to impulse and step loads have also been computed and the behaviours of the responses are analysed. Applying the double parametric form, it reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.

Uncertain dynamic responses of fuzzy fractionally damped beam using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads have been obtained. Gaussian fuzzy numbers are used to model the uncertainties. In the methodology using the alpha cut form, corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying double parametric form of fuzzy numbers. Finally, VIM has been applied to solve the same for the general fuzzy responses. Various numerical examples have been taken in to consideration.

The purpose of this study a fast procedure for the structural analysis of gas turbine blades in aircraft engines. In this connection, investigations on the behavior of gas turbine blades concentrate on the analysis and evaluation of starting dynamics and fatigue strength. Besides, the influence of structural mistuning on the vibration characteristics of the single blade is analyzed and discussed.

A basic computation cycle is generated from a flight profile to describe the operating history of the gas turbine blade properly. Within an approximation approach for high-frequency vibrations, maximum vibration amplitudes are computed by superposition of stationary frequency responses by means of weighting functions. In addition, a two-way coupling approach determines the influence of structural mistuning on the vibration of a single blade. Fatigue strength of gas turbine blades is analyzed with a semi-analytical approach. The progressive damage analysis is based on MINER’s damage accumulation assuming a quasi-stable behavior of the structure.

The application to a gas turbine blade shows the computational capabilities of the approach presented. Structural characteristics are obtained by robust and stable computations using a detailed finite element model considering different load conditions. A high quality of results is realized while reducing the numerical costs significantly.

The method used for analyzing the starting dynamics is based on the assumption of a quasi-static state. For structures with a sufficiently high stiffness, such as the gas turbine blades in the present work, this procedure is justified. The fatigue damage approach relies on the existence of a quasi-stable cyclic stress condition, which in general occurs for isotropic materials, as is the case for gas turbine blades.

Owing to the use of efficient analysis methods, a fast evaluation of the gas turbine blade within a stochastic analysis is feasible.

The fast numerical methods and the use of the full finite element model enable performing a structural analysis of any blade structure with a high quality of results.

The purpose of this paper is to present a semi-analytical solution for time-dependent natural convection flow with heat generation/absorption in an annulus partially filled with porous material.

The governing partial differential equations are transformed into the ordinary differential equations using the Laplace transform technique. The exact solution obtained is inverted from the Laplace domain to time domain using the Riemann-sum approximation approach. Justification of the Riemann-sum approximation approach is achieved by comparing the values obtained with those of the implicit finite difference method at both the transient state and the steady state at large time.

If is found that the peak axial velocity always occur in the clear fluid region. In addition, there is an indication that heat generating fluid is desirable for optimum mass flux in the annular gap most importantly when the convection current is enhanced by constant heat flux.

In view of the amount of works done on natural convection with internal heat generation/absorption, it becomes interesting to investigate the influence of this essential activity on natural convection flow in a vertical cylinder partially filled with porous material where the outer surface of the inner cylinder is either heated isothermally or with constant heat flux.

In semi-analytical modeling of spoke-type permanent-magnet (PM) machines (STPMM), the saturation effect is usually neglected (i.e. iron parts are considered to be infinitely permeable) and the PM magnetization is assumed tangential (i.e. magnetization pattern is considered to be tangential-parallel). This paper aims to present an improved two-dimensional (2D) subdomain technique for STPMM with the PM magnetization orientation in quasi-Cartesian coordinates by using hyperbolic functions considering non-homogeneous Neumann boundary conditions (BCs) in non-periodic regions and by applying the interfaces conditions (ICs) in both directions (i.e. t- and θ edges ICs).

The polar coordinate system is transformed into a quasi-Cartesian coordinate system. The rotor and stator regions are divided into primary subdomains, and a partial differential equation (PDE) is assigned to each subdomain. In the PM region, the magnetization orientation is considered in the equations. By applying BCs, the general solution of the equations is determined, and by applying the ICs, the corresponding coefficients are determined.

Using the proposed coordinate system, the general solution of PDEs and their coefficients can mathematically be simplified. The magnetic field and non-intrinsic unbalanced magnetic forces (UMF) calculations have been performed for three different values of iron core relative permeability (200, 800 and ∞), as well as different magnetization orientation values (135 and 80 degrees). The semi-analytical model based on the subdomain technique is compared with those obtained by the 2D finite-element analysis (FEA). Results disclose that the PM magnetization angle can affect directly the performance characteristics of the STPMM.

A new model for prediction of electromagnetic performances in the STPMM takes into account magnetization direction, and soft magnetic material relative permeability in a pseudo-Cartesian coordinate system by using subdomain technique is presented.