Structural analysis by a combined boundary element-transfer matrix method

A new approach, based on the combination of boundary element and transfer matrix methods, is proposed for two-dimensional problems. A transfer matrix is obtained, in this method, from the system of equations derived by the procedure based on the boundary element method. This method permits the use of a large number of elements, without getting involved with large matrices. A much smaller computer is, therefore, sufficient. Some numerical examples are presented to demonstrate the accuracy as well as the capability of the proposed method for solutions of two-dimensional problems.     

Full‐wave analysis of H‐plane waveguide junction loaded with metallic posts

A hybrid method that combines moment method and mode matching technique is presented to study H‐Plane waveguide discontinuity loaded with metallic posts at the junction of two waveguides. By expanding Eigen modes in waveguides, applying continuity of tangential fields at the discontinuity and finally nulling the tangential electric field on the post surface, a system of algebraic equations is solved to obtain current distribution on the posts and consequently scattering parameters of the structure. Then, as an application, an in‐line dual‐mode rectangular waveguide bandpass filter is analyzed using the proposed method along with generalized scattering matrix method. The numerical results are in good agreement with existing full wave finite element method in high frequency structure simulator (HFSS) results and measurements. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE , 2011.     

Analysis of propagation on open microstrip lines using mixed-order covariant projection vector finite elements

Many different procedures have been proposed for the finite element analysis of dielectric-loaded waveguiding structures. However, most of these approaches are unreliable because of the appearance of spurious modes. Mixed-order covariant projection finite elements have been shown to eliminate difficulties with spurious modes in vector waveguide formulations. The authors have developed a method to analyze open region dielectric-loaded waveguiding problems using mixed-order covariant projection finite elements. Details of the construction of the eigenvalue equation are presented. The treatment of open geometries using local absorbing boundary conditions is discussed. An efficient sparse eigensolver, based on iterative methods, that can solve the resulting nonlinear eigenvalue problem, is described. Analysis results are presented that demonstrate the ability of the formulation to solve for the propagating modes of open microstrip lines without the appearance of spurious modes.     

Shape-free polygonal hybrid displacement-function element method for analyses of Mindlin–Reissner plates

A high-performance shape-free polygonal hybrid displacement-function finite-element method is proposed for analyses of Mindlin–Reissner plates. The analytical solutions of displacement functions are employed to construct element resultant fields, and the three-node Timoshenko’s beam formulae are adopted to simulate the boundary displacements. Then, the element stiffness matrix is obtained by the modified principle of minimum complementary energy. With a simple division, the integration of all the necessary matrices can be performed within polygonal element region. Five new polygonal plate elements containing a mid-side node on each element edge are developed, in which element HDF-PE is for general case, while the other four, HDF-PE-SS1, HDF-PE-Free, IHDF-PE-SS1, and IHDF-PE-Free, are for the edge effects at different boundary types. Furthermore, the shapes of these new elements are quite free, i.e., there is almost no limitation on the element shape and the number of element sides. Numerical examples show that the new elements are insensitive to mesh distortions, possess excellent and much better performance and flexibility in dealing with challenging problems with edge effects, complicated loading, and material distributions.

     

A generalized geometrically nonlinear formulation with large rotations for finite elements with rotational degrees of freedoms

A generalized geometrically nonlinear formulation using total Lagrangian approach is presented for the finite elements with translational as well as rotational degrees of freedoms. An important aspect of the formulation presented here is that the restriction on the magnitude of the nodal rotations is eliminated by retaining true nonlinear nodal rotation terms in the definition of the element displacement field and the consistent derivation of the element properties based on this displacement field. The general derivation and the formulation steps are applicable to any element with translational and rotational nodal degrees of freedoms. The specific forms of the formulation for axisymmetric shells, two-dimensional isoparametric beams, curved shells, two-dimensional transition elements and solid-shell transition elements can be easily derived by considering the explicit forms of the nonlinear nodal rotations for the element at hand. The specific forms of this formulation have already been well tested and applied to various two- and three-dimensional elements, the results for some of which are presented here. Currently it is being applied to the three-dimensional isoparametric beam elements.     

Computation of optical modes in axisymmetric open cavity resonators

The computation of optical modes inside axisymmetric cavity resonators with a general spatial permittivity profile is a formidable computational task. In order to avoid spurious modes the vector Helmholtz equations are discretised by a mixed finite element approach. We formulate the method for first and second order Nédélec edge and Lagrange nodal elements. We discuss how to accurately compute the element matrices and solve the resulting large sparse complex symmetric eigenvalue problems. We validate our approach by three numerical examples that contain varying material parameters and absorbing boundary conditions (ABC).     

Higher order numerical solution of the integral equation for the two-dimensional neumann problem

Interest in the problem of two-dimensional potential flow in arbitrary multiply-connected domains has been stimulated by the need to calculate flow about multiple airfoil configurations consisting of slats and flaps detached from the main airfoil. General methods of solution are based on the use of a singularity distribution over the boundary. The distribution is obtained as the solution of an integral equation over the boundary. In implementing this solution various investigators approximate the boundary by an inscribed polygon, whose faces are small flat surface elements. The singularity on each element is taken as constant by some investigators and linearly varying by others. This paper systematically investigates the effectiveness of higher order approximations of the integral equation, including use of curved surface elements and parabolically-varying singularity. It is found that the approach using flat elements with constant singularity is mathematically consistent as is the next higher-order approach with parabolic elements and linearly varying singularity. The popular approach based on flat elements with linearly varying singularity is shown to be mathematically inconsistent, and examples are presented for which the effect of element curvature is greater than that of the singularity derivative. A number of examples are presented to show that: (1) the higher order solutions give very little increase in accuracy for the important case of exterior flow about a convex body: (2) for bodies with substantial concave regions and for interior flows in ducts, the use of parabolic elements and linearly varying singularity can give a dramatic increase in accuracy; and (3) the use of still higher order solutions leads to a rather small additional gain in accuracy.     

An improved three-dimensional full-vectorial finite-difference imaginary-distance beam propagation method

1 Introduction Recently, the importance of the planar lightwave circuits or photonic integrated cir- cuits (PLCs/PICs) has been widely recognized because the monolithic integration of various kinds of photonic or optoelectronic devices can be achieved via…     

An integration scheme for electromagnetic scattering using plane wave edge elements

Finite element techniques for the simulation of electromagnetic wave propagation are, like all conventional element based approaches for wave problems, limited by the ability of the polynomial basis to capture the sinusoidal nature of the solution. The Partition of Unity Method (PUM) has recently been applied successfully, in finite and boundary element algorithms, to wave propagation. In this paper, we apply the PUM approach to the edge finite elements in the solution of Maxwell’s equations. The electric field is expanded in a set of plane waves, the amplitudes of which become the unknowns, allowing each element to span a region containing multiple wavelengths. However, it is well known that, with PUM enrichment, the burden of computation shifts from the solver to the evaluation of oscillatory integrals during matrix assembly. A full electromagnetic scattering problem is not simulated or solved in this paper. This paper is an addition to the work of Ledger and concentrates on efficient methods of evaluating the oscillatory integrals that arise. A semi-analytical scheme of the Filon character is presented.     

Analysis of coupled anisotropic dielectric waveguides using the frequency domain finite-difference method

A rigorous general and versatile finite-difference formulation for the analysis of the propagation characteristics in structures, having the dielectric waveguide as the basic element, is presented here. In this formulation, the finite-difference method is used in the numerical solution of the scalar wave equation, written in terms of the transverse components of the magnetic field. As a result, a conventional eigenvalue problem is obtained without the presence of spurious modes (present in previous formulations), due to the implicit inclusion of the divergence of the magnetic field equal to zero. The general case of biaxial anisotropic dielectrics is considered, with the refractive index profile varying arbitrarily in the waveguide cross section. Dispersion characteristics for isolated and parallel coupled dielectric waveguides are calculated. The theoretical development was then used to solve particular problems and the results agree with those available from other methods. Results were obtained for a variety of waveguide structures of much interest, particularly for the development of integrated optics. © 1994 John Wiley & Sons. Inc.     

Generating contours on FEM/BEM higher-order surfaces using Java 3D textures

An efficient technique to visualize primary and secondary results for combined finite element method/boundary element method models as contours is presented. The technique is based on dividing higher-order surfaces into triangles and on using texture interpolation to produce contour plots. Since results of high accuracy with significant gradients can be obtained using sparse meshes of boundary elements and finite elements, special attention is devoted to element face subdivision. Subdivision density is defined on the basis of both face edge curvature and ranges of result fields over element faces. Java 3D API is employed for code development.     

A triangular finite difference scheme for large deflection problems

A lumped triangular element formulation is developed based on a finite difference approach for the large deflection analysis of plates and shallow shells. The presented formulation is independent of the boundary condition (unlike the finite difference formulation) and uses energy principles to derive a set of nonlinear algebraic equations which are solved by using an incremental Newton-Raphson iterative procedure. A study of the large deflection behaviour of thin plates is made for various edge conditions and aspect ratios, and the results obtained are compared with those using a finite element scheme. Representative nondimensional solutions for deflections and stresses are presented in the form of graphs.     

An alternative formulation of the geometric stiffness matrix for plate elements

A simplified formulation of the geometric stiffness matrix for plate elements is presented. In this formulation the transverse displacement is defined along the element boundary but not for the element interior as with the usual formulation. As such the formulation is particularly suitable for use with hybrid stress or discrete Kirchhoff methods which are also based on boundary approximation of the transverse displacement.

The simplicity, computational economy and accuracy obtained with the formulation compare favorably with the usual order formulation.     

Non-Reflecting Boundary Conditions for Maxwell’s Equations

A new discrete non-reflecting boundary condition for the time-dependent Maxwell equations describing the propagation of an electromagnetic wave in an infinite homogenous lossless rectangular waveguide with perfectly conducting walls is presented. It is derived from a virtual spatial finite difference discretization of the problem on the unbounded domain. Fourier transforms are used to decouple transversal modes. A judicious combination of edge based nodal values permits us to recover a simple structure in the Laplace domain. Using this, it is possible to approximate the convolution in time by a similar fast convolution algorithm as for the standard wave equation.     

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.     

A study of axisymmetric solid of revolution elements based on the assumed-stress hybrid model

A series of axisymmetric solid-of-revolution elements with 4-nodes and quadrilateral cross section have been developed based on the assumed-stress hybrid model. A linear boundary displacement assumption is employed for each element and a variety of interior stress assumptions have been made. Example problems of a thick cylinder under internal pressure and a thick sphere under internal pressure are utilized to evaluate the various elements, and several desirable stress assumptions have been identified. For the thick sphere problem, which involves a singularity problem as a result of the placing of an element at the axis of symmetry, several special treatments are suggested. Comparisons of present results with those obtained by the use of a 4-node element based on the assumed displacement model indicate that the present hybrid elements are far superior in predicting the stress distribution within the elements.     

An analysis of,and remedies for,kinematic modes in hybrid-stress finite elements: selection of stable,invariant stress fields

In this paper a study of the existence of spurious kinematic modes in hybrid-stress finite elements, based on assumed equilibrated stresses and compatible boundary displacements, and the resulting rank-deficiency of the element stiffness matrix, is presented. A method of selection of least-order, stable, invariant, stress fields is developed so as to ensure the prevention of kinematic modes. A 20-node cubic element, a 8-node cubic element and a 4-node square, based on assumed equilibrated stresses within the element and compatible displacements at the boundary of the element, are discussed for purposes of illustration. Comments are made on the generality of the present method, which is based on group theoretical arguments.     

The laplace transform DBEM for mixed-mode dynamic crack analysis

A boundary element method (BEM) for the two-dimensional analysis of structures with stationary cracks subjected to dynamic loads is presented. The difficulties in modelling the structures with cracks by BEM are solved by using two different equations for coincident points on the crack surfaces. The equations are the displacement and the traction boundary integral equations. This method of analysis requires discretization of the boundary and the crack surfaces only. The time-dependent solutions are obtained by the Laplace transform method, which is used to solve several examples. The influence of the number of boundary elements and the number of Laplace parameters is investigated and a comparison with other reported solutions is shown.     

Structural damage identification for thin plates using smart piezoelectric transducers

An impedance-based structural damage identification method for thin plates is presented in this paper using piezoelectric ceramic (PZT) transducers. The local damages are characterized by introducing a damage parameter in each finite element. A two-dimensional electromechanical impedance model is proposed to predict the electric admittance of the PZT transducer bonded to the plates. The general equations for generating structural dynamic stiffness from normal modes are formulated based on finite element analysis. The first-order perturbation method is introduced to obtain the electric admittance change on PZT transducers due to damage. A damage identification scheme for solving nonlinear optimization problem is proposed to locate and quantify the damage by matching the numerical and experimental electric admittance change on PZT transducers. The proposed technique is verified through numerically simulated damage identification tests.     

Optimization-oriented design of rectangular and circular waveguide components with the use of efficient mode-matching simulators in commercial circuit CAD tools (invited article)

Efficient mode-matching waveguide building blocks are described for user-friendly utilization in common commercial circuit CAD tools. This hybrid mode-matching/circuit theory CAD approach allows the accurate, convenient, and fast design of a comprehensive class of rectangular and/or circular waveguide components, such as filters, transformers, and multiplexers by advantageously combining the accuracy of the rigorous electromatic simulators with the efficiency of mature and well-established circuit theory design instruments. Moreover, an adequate multimode combination technique between the individual elements enables the utilization of additional design parameters resulting from higher-order mode interaction effects. The efficiency of the hybrid CAD method is demonstrated at typical microwave design examples that are optimized by use of the mode-matching waveguide building blocks in powerful commercial CAD packages, such as hp-EEsof's Touchtone ^TM or Libra ^TM and OSA's Osa 90/hope^TM. Advanced high-power asymmetrical iris coupled TE₁₀₃/TE₂₀₁ filters with high edge steepness show that the presented hybrid method is also applicable to more specialized design tasks. Its accuracy is verified by measurements and by comparison with the results of the conventional mode-matching/modal scattering matrix technique. © 1997 John Wiley & Sons, Inc. Int J Microwave Millimeter-Wave CAE 7: 37–51, 1997.