Layered Finite Element Method Research Articles

Efficient Thermal Analysis of Integrated Circuits and Packages With Microchannel Cooling Using Laguerre-Based Layered Finite Element Method

In this article, an efficient approach named Laguerre-based layered finite element method (LB-LFEM) is presented for transient thermal analysis of integrated circuits (ICs) and packages with microchannel cooling. A marching-on-in-order scheme based on weighted Laguerre polynomials is employed to deal with the governing equations of conjugate heat transfer, where the time variables are eliminated by the orthogonality of Laguerre basis functions. Then, the layered finite element method is utilized to model complex geometries and reduce the original system matrix to that only involves two-dimensional (2-D) surface unknowns in each layer. Based on the reduced matrix equation, the Laguerre coefficients are solved recursively order by order. The computational efficiency is improved significantly by this means. The validity and high efficiency of LB-LFEM are demonstrated by several examples.

An efficient layered finite element method with domain decomposition for simulations of resistivity well logging

A novel layered finite element scheme combined with domain decomposition method is proposed for fast simulations of resistivity well logging. The recently developed layered finite element scheme employs a 2D discretization to the cross section of a 3D layered structure, and exploits the piecewise homogeneity within each layer in an analytical way with high accuracy. Combining this layered finite element method with domain decomposition strategy leads to a new scheme with further improved modeling flexibility and efficiency. Each layer of a stratified structure will be treated as a subdomain and discretized independently. Nonconforming meshes are allowed between adjacent layers, which makes the discretization very flexible, and saves a great number of unknowns compared with conventional finite element discretizations with conforming meshes. The proposed method can be easily hybridized with conventional finite element schemes, and this combination is especially suitable for modeling layered problems with local inhomogeneities, such as resistivity logging with borehole washouts in some layers. Numerical examples including a 28-layer Oklahoma formation and a washed-out layered borehole model are given to demonstrate the validity and efficiency of this method.

Parametric and comparative study of spandrel beam effect on the punching shear strength of reinforced concrete flat plates

SUMMARYThe safe and efficient construction of reinforced concrete flat plate systems requires an accurate, reliable and universally applicable procedure for the punching shear strength design. A nonlinear layered finite element method (LFEM) capable of analysing the punching shear strength of such system has been developed. Based on the LFEM, a parametric study is undertaken to evaluate some of the factors influencing punching shear strength of reinforced concrete flat palate with spandrel beams. This is done by varying the depth and the width of the spandrel beam while keeping other variables constant. The numerical results obtained by the LFEM are also compared with those predicted by the recommendations of the Australian Standard (AS3600‐2009) and the Wollongong‐Griffith (W‐G) semi‐empirical method. The results confirm that the Australian Standard is inadequate in predicting the punching shear strength at the corner and edge column connections of flat plates with spandrel beams or torsion strips. Copyright © 2010 John Wiley & Sons, Ltd.

Fast Iterative Solution Algorithms in the Frequency-Domain Layered Finite Element Method for Analyzing Integrated Circuits

Fast algorithms are developed in this work for solving the system matrix resulting from a frequency-domain layered finite element based analysis of integrated circuits. The frequency-domain layered finite element method represents a 3-D layered system by a 2-D layered system, and further by a single-layered one. The reduced system matrix is generally denser than the original sparse matrix. In this paper, we show that 1) the dense matrix-vector multiplication can be performed in linear complexity; in addition, the reduction cost can be bypassed, 2) an effective preconditioner can be developed to converge the iterative solution of the reduced system matrix in a small number of iterations, and 3) the preconditioner can be solved in linear complexity. As a result, the reduced system matrix can be solved efficiently. The algorithms are rigorous without making any approximation. They apply to any arbitrarily-shaped multilayer structure. Numerical results demonstrated the accuracy, effectiveness, and efficiency of the proposed algorithms in analyzing on-chip circuits.

Ultimate strength analysis of normal and high strength concrete wall panels with varying opening configurations

Currently the wall panel design equations given in the Australian Standard and the American Institute Code offer no guidelines for the inclusion of side restraints or openings. Empirical formulae have been derived based upon limited test data, in which only the length and location of openings are accounted for with a dimensionless parameter, α x . In this study the nonlinear Layered Finite Element Method (LFEM) is used to undertake a comparative study to verify the effectiveness of the method in predicting the failure characteristics of seven two-way normal strength concrete walls without and with window and door openings. The ultimate loads, load–deflection responses up to failure, deflected shapes and crack patterns predicted by the LFEM are compared to the experimental observations. The method is then used to conduct three parametric studies investigating the influence of opening size, length and height on the ultimate load and deflection of twenty high strength wall panels acting in both one-way and two-way. Comparisons of the numerical results to established formula for walls with openings validated the accuracy of the LFEM predictions. Results demonstrate that increase in opening size decreases the axial strength ratio to different degrees for one-way and two-way walls. Increasing only the opening length also significantly decreases the axial strength ratio. Increasing only the opening height has little impact on the ultimate load capacity. Walls analysed in two-way action have an increased strength compared to the one-way counterparts due to the provision of side restraints, however, such improved strength becomes small for a large sized opening. Results further confirm that increasing the opening height together with the length has the most critical effect. Hence to ensure safe design, the combined effects of increasing both the height and length of an opening should be incorporated into the ultimate load formula which is proposed in this study. The results of this study have assisted in verifying the LEFM as a reliable and effective technique for determining a relationship between ultimate load capacity and varying opening configurations so that more dependable design aids and accurate formulae can be established.

Fast Reduction Algorithms in the Frequency-Domain Layered Finite Element Method for the Electromagnetic Analysis of Large-Scale High-Frequency Integrated Circuits

In this paper, fast algorithms are proposed for an efficient reduction of a 3-D layered system matrix to a 2-D layered one in the framework of the frequency-domain layered finite element method. These algorithms include: 1) an effective preconditioner <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</b> that can converge the iterative solution of the volume-unknown-based matrix equation in a few iterations; 2) a fast direct computation of <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</b> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> in linear complexity in both CPU run time and memory consumption; and 3) a fast evaluation of <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</b> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> in linear complexity, with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> being an arbitrary vector. With these fast algorithms, the volume-unknown-based matrix equation is solved in linear complexity with a small constant in front of the number of unknowns, and hence significantly reducing the complexity of the 3-D to 2-D reduction. The algorithms are rigorous without making any approximation. They apply to any arbitrarily-shaped multilayer structure. Numerical and experimental results are shown to demonstrate the accuracy and efficiency of the proposed algorithms.

Prediction of Punching Shear Failure Behaviour of Slab-Edge Column Connections with Varying Opening and Column Parameters

A numerical analysis using the non-linear Layered Finite Element Method (LFEM) is undertaken to predict the effect of openings on punching shear failure behaviour of slab-column connections with shear stud reinforcement (SSR). In all, twenty one (21) models are examined through six parametric studies including varying the opening size and location and varying the column aspect ratio. The numerical results covering the load-deflection response, ultimate shear strength, deformation and crack pattern are evaluated in some detail. Where applicable the predicted ultimate shear strengths are compared to the experimental results. Also included in the comparison are the empirical predictions recommended by the Standards Association of Australia and the American Concrete Institute. This investigation is an important step towards the determination of the size and location of opening and the size of column for optimum structural performance of flat plate systems.

Finite element studies of reinforced concrete slab - edge column connections with openings

An extended nonlinear layered finite element method (LFEM) is used to investigate the influence of openings and shear stud reinforcement (SSR) on the behaviour of reinforced concrete slab – edge column connections. In all, ten large-scale slab – edge column connections tested previously are analyzed. The laboratory test variables were the size and location of the openings in the vicinity of an edge column and the existence of SSR. The numerical results of the load–deflection response, the ultimate strength, and the crack patterns are compared with the experimental findings and good agreement is achieved. A numerical study on two connections is also carried out to determine the influence of the locations of opening in slab – edge column connections with SSR. Discussion on code provisions for slabs with openings is provided. The comparative and numerical studies confirm the accuracy, reliability, and effectiveness of the LFEM in the analysis of slab – edge column connections with both openings and SSR.Key words:slab–column connection, punching shear, opening, shear stud reinforcement, finite element analysis.

Layered Finite Element Analysis of One-Way and Two-Way Concrete Walls with Openings

Empirical wall design equations provided in major codes of practice are conservative because they do not cover walls that are supported on all four sides or walls with slenderness ratios greater than 30. They do not cover walls that require openings for doors, windows and services. The recognition of such factors in design codes would result in savings in construction costs. This study investigates the effect of side restraints and the presence of openings for reinforced concrete wall panels where axial load eccentricity induces secondary bending. A numerical analysis of such walls is undertaken using the non-linear Layered Finite Element Method (LFEM), and results are compared with eight one-third to one-half scale wall panels tested previously at Griffith University. The LFEM predicts the failure loads, the load-deflection responses, the deformed shapes and the crack patterns of the tested wall panels. Subsequent parametric studies on the ultimate load carrying capacity of 54 one-way and two-way reinforced concrete walls with openings established relationships of failure load with slenderness ratio and eccentricity.

Structural assessment of externally flexural strengthened reinforced concrete beam after repaired with polymer mixture

This study investigated the effectiveness of external strengthening technique. The experimental variables were the strengthening material and overlay materials using polymer mixtures. Beams considered in this study are the ones strengthened either with external steel plate or carbon fiber sheet (CFS) bonded to the overlay soffit or with reinforcing rebars in the overlay. An analytical method based on the nonlinear layered finite element method is used to simulate the load–deflection behavior of strengthened beam. The theoretically obtained load–deflection relationships and strains of the strengthened beams are compared to the corresponding experimental values. Efficiencies of the repairing techniques are evaluated by comparing the approximate measures on the cumulative slips. Parametric studies are then obtained using the developed model to investigate the effects of design variables on the overall flexural behavior of the strengthened beam. Simply supported beams under monotonically increasing symmetrical loads are considered exclusively.

Failure analysis of column–slab connections with stud shear reinforcement

The design of a flat plate structure is generally governed either by serviceability limits on deflection or punching shear strength of the column–slab connections. To increase the strength of a column–slab connection, a new type of shear reinforcement, referred to as shear stud, is gaining popularity in practice. In this paper, a nonlinear layered finite element method (LFEM) is used to investigate the effectiveness of the shear studs in increasing the punching shear strength of edge and corner column–slab connections. In total, nine large-scale reinforced concrete slabs of a flat plate floor in the vicinity of edge and corner columns, tested previously in the laboratory, are analysed. All the slabs contained stud shear reinforcement (SSR) except a control slab where no SSR was provided. The test variables were the column size and the ratio of stud spacing to slab thickness. The punching shear strengths, load–deflection responses, and crack patterns predicted by the LFEM are compared with the experimental results. The numerical investigation confirms the accuracy and effectiveness of the LFEM in predicting the strength of column–slab connections with SSR.Key words: column–slab connection, concrete flat plate, punching shear, stud shear reinforcement, finite element analysis.

Free vibration analysis of stiffened laminated plates using layered finite element method

The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.

Cracking and Punching Shear Failure Analysis of RC Flat Plates

This paper presents a nonlinear layered finite element method capable of analyzing cracking and punching shear failure of reinforced concrete flat plates with spandrel beams or torsion strips. Incorporating a layered approach with transverse shear capabilities, the procedure takes into account the full interaction between the spandrel beam and the adjoining slab (in bending, shear, and torsion). The formulation of the nonlinear cracking and failure analysis is discussed in some detail. A comparative study based on a series of 11 half-scale reinforced concrete flat plate models and four single slab-column specimens confirms the method's ability to satisfactorily predict the punching shear strengths, the deflections, and the crack patterns, as well as the collapse loads, of the models. Also included in the comparison is a semiempirical procedure, along with those recommended by the American Concrete Institute, the British Standards Institution, and the Standards Association of Australia. Results show that t...

Layered finite element method in cracking and failure analysis of RC beams and beam-column-slab connections

A nonlinear semi-three-dimensional layered finite element procedure is developed for cracking and failure analysis of reinforced concrete beams and the spandrel beam-column-slab connections of flat plates. The layered element approach takes the elasto-plastic failure behaviour and geometric nonlinearity into consideration. A strain-hardening plasticity concrete model and a smeared steel model are incorporated into the layered element formulation. Further, shear failure, transverse reinforcement, spandrel beams and columns are successfully modelled. The proposed method incorporating the nonlinear constitutive models for concrete and steel is implemented in a finite element program. Test specimens including a series of reinforced concrete beams and beam-column-slab connections of flat plates are analysed. Results confirm the effectiveness and accuracy of the layered procedure in predicting both flexural and shear cracking up to failure.

Analysis of Failure Modes for Reinforced Concrete Slabs Under Impulsive Loads

The faillure modes that can be associated with soft impulsive loads for reinforced concrete slabs are analytically predicted using a nonlinear dynamic layered finite element method. The failure mechanism at the ultimate states is also predicted and found to be in good agreement with the actual phenomenon. The effects of loading rates during impulsive loadings are also considered, and it is found that the failure modes are affected by the loading rates and also impulse from an impulsive load function. The failure modes can be predicted using the proposed analytical method. The failure modes can be classified into three different regions based on the loading rates. It can be concluded that this method may be used in future as a tool for a dynamic design method for reinforced concrete structure under soft impulsive loads.

Effective widths of composite beams with ribbed metal deck

The effective width of the concrete slab of a composite beam is used in the determination of its moment resistance and service load moment for the purposes of structural design of the composite beam. It is usually assumed that the same effective width of the concrete slab may be used for both ultimate strength and elastic stage calculations.This paper presents the results of an analytical investigation of the variation of the effective width of composite beams and ribbed slabs formed by ribbed metal deck in both the elastic and inelastic stages and at ultimate load. A layered finite element method is used to model the composite beam. The influence of four variables on the effective width of the composite beams was studied, namely, type of loading, beam span to actual concrete slab width, ultimate compressive strength of the concrete, and steel beam size.It was found that the effect of the compressive strength of the concrete and the size of the steel beam have negligible influence on the effective width of the concrete slab. The effective width of the slab at ultimate load is of the order of 4% larger than that in the elastic range.The effective width used for the design of composite beams under a uniformly distributed load, which is the practical loading in most cases, is significantly different from that which should be used for any other type of loading.

3-D Dynamic Analysis And Computer GraphicsApplication To Impact Failure Simulation ForReinforced Concrete Slabs

A 3-D (three-dimensional) nonlinear dynamic layered finite element method is applied to evaluate the ultimate behavior and failure modes of reinforced concrete slabs under soft impact loads. In order to propose a practical impact resistance evaluation method for reinforced concrete slab structures, computer graphics (CG) is used as a visualization technique to simulate impact failure behavior of reinforced concrete slabs until post-failure range was reached based on the analytical results during impact loading.