A comparative study between shielded and open coplanar waveguide discontinuities

A comparative study between open and shielded coplanar waveguide (CPW) discontinuities is presented. In this study, the space domain integral equation method is used to characterize several discontinuities such as the open-end CPW and CPW series stubs. Two different geometries of CPW series stubs (straight and bent stubs) are compared with respect to resonant frequency and radiation loss. In addition, the encountered radiation loss due to different CPW shunt stubs is evaluated experimentally. The notion of forced radiation simulation is presented, and the results of such a simulation are compared to the actual radiation loss obtained rigorously. It is shown that such a simulation cannot give reliable results concerning radiation loss from printed circuits.     

Analysis of a radial drilling machine structure using finite element method

In the present paper an attempt has been made to study the behaviour of the structure of a radial drilling machine due to static loads using beam finite elements. In calculating the stiffness of the beam element the warping effects of the cross section has also been included. Using “front solution” technique, the whole machine tool structure has been analysed for different combinations of the cross sections of the radial arm and the column. From this study a best cross section for the structure of the machine has been suggested.     

Analysis of electromagnetic waveguide bends by three-dimensional finite element method with edge elements

An approach based on the finite element method (FEM) with the rectangular-parallelepipd edge element is proposed for the analysis of electromagnetic waveguide bends. Here, to be permissible for analysis of various electromagnetic waveguides, the analytical relations in the uniform waveguide are constructed numerically by using the FEM with the rectangular edge element. To confirm the validity and versatility of this approach, bends of a hollow waveguide, a half-filled dielectric waveguide, and a finline are analyzed. © 1996 John Wiley & Sons, Inc.     

Analysis of nonlinear, dynamic coupled thermoviscoelasticity problems by the finite element method

This investigation deals with the numerical solution of a class of nonlinear problem in transient, coupled, thermoviscoelastidty. Equations of motion and heat conduction are derived for finite elements of thermomechanically simple materials and these are adapted to special classes of thermorheologically simple materials. The analysis involves the solution of large systems of nonlinear integrodifferential equations in the nodal displacements and temperatures and their histories. As a representative example, the general equations are applied to the problem of transient response of a thick-walled hollow cylinder subjected to time-varying internal and external pressures, temperatures, and heat fluxes. The integration scheme used to solve the nonlinear equations employs a linear acceleration assumption, representation of nonlinear integral terms by Simpson's rule, and the iterative solution of large systems of nonlinear algebraic equations at each reduced time step by the Newton-Raphson method. Various numerical results are given and are compared with the linearized, isothermal, and quasi-static solutions.     

Calculation of a parallel-plate waveguide with a chiral insert by the mixed finite element method

A parallel-plate waveguide with metallic boundaries, containing an insert of a chiral substance, is considered. The field distribution inside the insert is studied when the system is excited by the guide’s normal wave incident on the insert. The problem is considered in the full vector formulation. The waveguide is calculated by the mixed finite element method, which makes it possible to avoid spurious modes (so-called spirits).     

Solving Wick-stochastic water waves using a Galerkin finite element method

A Galerkin finite element approximation of Wick-stochastic water waves is developed and numerically investigated. The problems under study consist of a class of shallow water equations driven by white noise. Random effects may appear in the water free surface or in the bottom topography among others. To perform a rigorous study of stochastic effects in the shallow water equations we employ techniques from Wick calculus. The differentiation respect to time and space along with the product operations are performed in a distribution sense. Using the Wiener-Itô chaos expansion for treating the randomness, the governing equations are transformed into a sequence of deterministic shallow water equations to be solved for each chaos coefficient by standard methods from computational fluid dynamics. In our study, we formulate a finite element method for spatial discretization and a backward Euler scheme for time integration. Once the chaos coefficients are obtained, statistical moments for the stochastic solution are carried out. Numerical results are presented for stochastic water waves in the Strait of Gibraltar.     

On the use of a modified Newton method for nonlinear finite element analysis

In this paper, the usefulness of modified Newton methods for solving certain minimization problems arising in nonlinear finite element analysis is investigated. The application considered is nonlinear elasticity, in particular geometrically nonlinear shells. On a test problem, it is demonstrated that a particular implementation of a modified Newton method using both descent directions and directions of negative curvature is able to identify a minimizer, whereas an unmodified Newton method and modified Newton methods using only descent directions fail to converge to the minimizer. The use of modified Newton methods is suggested as a useful complement to the present continuation methods used for nonlinear finite element analysis.     

CAD-oriented formulas for the quasi-tem parameters of shielded and semi-enclosed (coupled) coplanar waveguides

On the magnetic-wall approximation for their slots, shielded coplanar waveguides (SCPWs) and semienclosed CPWs (SECPWs) are analyzed through an intensive use of elliptic function transformation. CAD-oriented formulas for the quasi-TEM parameters of SCPWs and SECPWs, including their coupled versions, are derived. The comparison of the results calculated here with previous ones show 2% accuracy for formulas in the practical situation where the slots are not too wide, e.g., s / (s + 2w) ≥ 0.2 for an SCPW. © 1994 John Wiley & Sons, Inc.     

Buckling analysis of imperfect frames using a stochastic finite element method

A stochastic finite element method is developed for the buckling analysis of frames with random initial imperfections, uncertain sectional and material properties. The random geometrical imperfections of the frames are described by member initial crookednesses which are modeled as given initial displacement functions with amplitudes treated as random variables. The effects of the random initial geometric imperfections are formulated as a set of equivalent random nodal coordinates in the finite element discretization of the members. The mean-centered second-order perturbation technique is used to formulate the stochastic finite element method for the buckling analysis of the imperfect frames. Use of the present method is illustrated by several examples of buckling analysis of random frames. Results derived from the Monte Carlo method are also obtained for comparison.     

Wave propagation in mechanical waveguide with curved members using wave finite element solution

In this paper, wave propagation in straight and curved mechanical waveguide is investigated. The main objective of the study is to develop a numerical model that can determine the response of the intact or damaged waveguide structure which is subjected to the incident waves. The wave finite element method, which is based on the simple development of standard finite element procedures, is used for the extraction of eigenmodes and analysis of the wave propagation properties. To make an effective use of those eigenmodes, a criterion that is based on the properties of eigensolutions is proposed to condense the mode bases. By using the reduced eigenmode bases, the high frequency wave motion due to the presence of curved part in the waveguide is examined through the wave propagation approach. Numerical analysis indicates that, in order to choose the appropriate wave modes for inspection, it is necessary to obtain both the eigenmode and wave propagation properties, thus the incident wave could be optimised for better monitoring of the structural features and detection of the local damages.     

Optimization design of multi-material micropump using finite element method

This paper presents a micropump fabricated from low cost materials with specific goal of cost reduction. The micropump does not require any valve flap and comprises one plastic pump polyether–ether–ketone (PEEK) body, one metal diaphragm, and three piezoelectric ceramics to form piezoelectrically actuated diaphragm valves. The valve actuation simplifies micropump structural designs and assembly processes to make the pump attractive for low cost bio-medical drug delivery applications. A detailed optimization design of geometric parameters of the piezoelectrically actuated diaphragm is undertaken by use of 3D finite element method (FEM) to maximize piezoelectric actuation capability and ensure actuation reliability. An optimized geometric dimensional design: the ratio of thicknesses between the piezoelectric ceramics and the metal diaphragm, and the lateral dimension of the piezoelectric ceramic, is obtained through simulations. Based on the optimized design, a good agreement has been reached between simulated and measured strokes of the micropumps. The tested results show that the micropump has a high pump flow rate for air, up to 39 ml/min, and for water, up to 1.8 ml/min, and is capable of ensuring diaphragm’s maximum stress and strain is within material strength for reliable work.     

Nonlinear bending of beams using the finite element method

In this paper a finite element formulation for determining the finite deflection of thin bars is presented. The nonlinear stiffness equations are generated after simple approximate expressions involving the nodal parameters are used to replace the nonlinear terms in the energy functional. The procedure used results in a simplified set of nonlinear algebraic equations which are more amenable to solution than the equations usually presented. The applicability and accuracy of the method together with an evaluation of three incremental solution techniques, a step by step method, a one step Newton-Raphson procedure, and a variable interpolation technique is demonstrated by solving a cantilever beam with a point load acting on the end. Curves showing the sensitivity to increment size and to the number of elements are also presented. The results indicate that the formulation is accurate and inexpensive in terms of computational effort.     

Damage detection of structures using spectral finite element method

This paper brings together the principles, equations, and applications of damage modelling and elastic waves propagation, both traditional and state-of-the-art in a review form. It begins with the relevant fundamentals of damage modelling, derives the basic equations of fracture mechanics and elastic wave propagations, and covers advanced topics and applications of Lamb waves that are at the forefront of today’s research. The results obtained indicate that the current approach is capable of detecting cracks and delaminations of very small size, even in the presence of considerable measurement errors. The sections are filled with case studies, worked examples and exercises that make this paper an outstanding resource.     

CAD model of a gap in a coplanar waveguide

The partial capacitance approach and conformal mapping techniques are used to evaluate simple closed-form models for parallel and series capacitances of equivalent π-network of a symmetric gap in a CPW. Models are compared with experimental data and full wave analysis. They are useful for a wide range of CPW parameters and frequencies. © 1996 John Wiley & Sons, Inc.     

Analysis of a typical shaped tunnel lining by finite element method

In the present study, the diversion tunnel of Tehri Dam in India has been analyzed using finite element procedure. The tunnel is of circular shape from inside, from hydraulic considerations, and of horseshoe shape from outside, to facilitate excavation and construction of the tunnel. In the analysis, the 8-noded parabolic elements have been used and shape functions are chosen as to satisfy the continuity of displacements between the elements and the convergence criterion. A parametric study has been carried out and the results are presented in nondimensional form and are compared with results of conventional analysis of circular cross sections.     

Design multiple-layer gradient coils using least-squares finite element method

The design of gradient coils for magnetic resonance imaging is an optimization task in which a specified distribution of the magnetic field inside a region of interest is generated by choosing an optimal distribution of a current density geometrically restricted to specified non-intersecting design surfaces, thereby defining the preferred coil conductor shapes. Instead of boundary integral type methods, which are widely used to design coils, this paper proposes an optimization method for designing multiple layer gradient coils based on a finite element discretization. The topology of the gradient coil is expressed by a scalar stream function. The distribution of the magnetic field inside the computational domain is calculated using the least-squares finite element method. The first-order sensitivity of the objective function is calculated using an adjoint equation method. The numerical operations needed, in order to obtain an effective optimization procedure, are discussed in detail. In order to illustrate the benefit of the proposed optimization method, example gradient coils located on multiple surfaces are computed and characterised.     

Static stress analysis of a composite bevel gear using a three-dimensional finite element method

The possibility of using composite materials for power transmission spur gear, from a static strength point of view, have been proved by the authors in their previous study. In this present work an attempt has been made to study the behaviour of composite bevel gear from a static load point of view using a three-dimensional finite element method. The performance of two composite material bevel gears are presented and compared with a carbon steel gear. From a static strength point of view a glass epoxy bevel gear is slightly closer to a carbon steel bevel gear than a boron/epoxy bevel gear; but from a displacement point of view glass/epoxy deviates from that of carbon steel much more than boron/epoxy, unlike the case of a composite spur gear, where boron/epoxy was better both from strength and displacement points of view. Hence from the results it is concluded that composite materials such as boron/epoxy can be very much thought of as a material for power transmission bevel gears.     

Nonlinear analysis of skew plates using the finite element method

In this paper finite element analysis of the large deflection behaviour of skew plates has been done. A high precision conforming triangular plate bending element has been used. The central deflection, bending and membrane stresses have been reported for simply supported and clamped rhombic plates. The variations of these quantities have been studied for different skew angles.     

Topology optimization using the p-version of the finite element method

A multiresolution topology optimization approach is proposed using the p-version finite element method (p-version FEM). Traditional topology optimization, where a density design variable is assigned to each element, is suitable for low-order h-version FEM. However, it cannot take advantage of the higher accuracy of higher-order p-version FEM analysis for generating results with higher resolution. In contrast, the proposed method separates density variables and finite elements so that the resolution of the density field, which defines the structure, can be higher than that of the finite element mesh. Thus, the method can take full advantage of the higher accuracy of p-version FEM.