A finite element modelling method for thin layer mortared masonry systems

This paper deals with a finite element modelling method for thin layer mortared masonry systems. In this method, the mortar layers including the interfaces are represented using a zero thickness interface element and the masonry units are modelled using an elasto-plastic, damaging solid element. The interface element is formulated using two regimes; i) shear-tension and ii) shearcompression. In the shear-tension regime, the failure of joint is consiedered through an eliptical failure criteria and in shear-compression it is considered through Mohr Coulomb type failure criterion. An explicit integration scheme is used in an implicit finite element framework for the formulation of the interface element. The model is calibrated with an experimental dataset from thin layer mortared masonry prism subjected to uniaxial compression, a triplet subjected to shear loads a beam subjected to flexural loads and used to predict the response of thin layer mortared masonry wallettes under orthotropic loading. The model is found to simulate the behaviour of a thin layer mortated masonry shear wall tested under pre-compression and inplane shear quite adequately. The model is shown to reproduce the failure of masonry panels under uniform biaxial state of stresses.

An explicit finite element modelling method for masonry walls under out-of-plane loading

An explicit finite element modelling method is formulated using a layered shell element to examine the behaviour of masonry walls subject to out-of-plane loading. Masonry is modelled as a homogenised material with distinct directional properties that are calibrated from datasets of a “C” shaped wall tested under pressure loading applied to its web. The predictions of the layered shell model have been validated using several out-of-plane experimental datasets reported in the literature. Profound influence of support conditions, aspect ratio, pre-compression and opening to the strength and ductility of masonry walls is exhibited from the sensitivity analyses performed using the model.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Comparison of eight published lumbar spine finite element models

Due to its ability to represent intricate systems with material nonlinearities as well as irregular loading, boundary, geometrical and material domains, the finite element (FE) method has been recognized as an important computational tool in spinal biomechanics. Current FE models generally account for a single distinct spinal geometry with one set of material properties despite inherently large inter-subject variability. The uncertainty and high variability in tissue material properties, geometry, loading and boundary conditions has cast doubt on the reliability of their predictions and comparability with reported in vitro and in vivo values. A multicenter study was undertaken to compare the results of eight well-established models of the lumbar spine that have been developed, validated and applied for many years. Models were subjected to pure and combined loading modes and their predictions were compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges; their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with previously published median in vitro values. However, the ranges of predictions were larger and exceeded the in vitro ranges, especially for facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with in vivo values. The simulations yielded median facet joint forces of 0 N in flexion, 38 N in extension, 14 N in lateral bending and 60 N in axial rotation that could not be validated due to the paucity of in vivo facet joint forces. In light of high inter-subject variability, one must be cautious when generalizing predictions obtained from one deterministic model. This study demonstrates however that the predictive power increases when FE models are combined together. The median of individual numerical results can hence be used as an improved tool in order to estimate the response of the lumbar spine.

Wavelet based spectral finite element modelling and detection of de-lamination in composite beams

In this paper, a model for composite beam with embedded de-lamination is developed using the wavelet based spectral finite element (WSFE) method particularly for damage detection using wave propagation analysis. The simulated responses are used as surrogate experimental results for the inverse problem of detection of damage using wavelet filtering. The WSFE technique is very similar to the fast fourier transform (FFT) based spectral finite element (FSFE) except that it uses compactly supported Daubechies scaling function approximation in time. Unlike FSFE formulation with periodicity assumption, the wavelet-based method allows imposition of initial values and thus is free from wrap around problems. This helps in analysis of finite length undamped structures, where the FSFE method fails to simulate accurate response. First, numerical experiments are performed to study the effect of de-lamination on the wave propagation characteristics. The responses are simulated for different de-lamination configurations for both broad-band and narrow-band excitations. Next, simulated responses are used for damage detection using wavelet analysis.

Influence of Crown Ferrule Heights and Dowel Material Selection on the Mechanical Behavior of Root-Filled Teeth: A Finite Element Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Finite element analysis predicts experimental failure patterns in vertebral bodies loaded via intervertebral discs up to large deformation

Vertebral compression fracture is a common medical problem in osteoporotic individuals. The quantitative computed tomography (QCT)-based finite element (FE) method may be used to predict vertebral strength in vivo, but needs to be validated with experimental tests. The aim of this study was to validate a nonlinear anatomy specific QCT-based FE model by using a novel testing setup. Thirty-seven human thoracolumbar vertebral bone slices were prepared by removing cortical endplates and posterior elements. The slices were scanned with QCT and the volumetric bone mineral density (vBMD) was computed with the standard clinical approach. A novel experimental setup was designed to induce a realistic failure in the vertebral slices in vitro. Rotation of the loading plate was allowed by means of a ball joint. To minimize device compliance, the specimen deformation was measured directly on the loading plate with three sensors. A nonlinear FE model was generated from the calibrated QCT images and computed vertebral stiffness and strength were compared to those measured during the experiments. In agreement with clinical observations, most of the vertebrae underwent an anterior wedge-shape fracture. As expected, the FE method predicted both stiffness and strength better than vBMD (R2 improved from 0.27 to 0.49 and from 0.34 to 0.79, respectively). Despite the lack of fitting parameters, the linear regression of the FE prediction for strength was close to the 1:1 relation (slope and intercept close to one (0.86 kN) and to zero (0.72 kN), respectively). In conclusion, a nonlinear FE model was successfully validated through a novel experimental technique for generating wedge-shape fractures in human thoracolumbar vertebrae.

Parametric Analysis of Effective Material Properties of Thickness-Shear Piezoelectric Macro-Fibre Composites

A previous study on the characterization of effective material properties of a d(15) thickness-shear piezoelectric Macro-Fibre Composite (MFC) made of seven layers (Kapton, Acrylic, Electrode, Piezoceramic Fibre and Epoxy Composite, Electrode, Acrylic, Kapton) using a finite element homogenization method has shown that the packaging reduces significantly the shear stiffness of the piezoceramic material and, thus, leads to significantly smaller effective electromechanical coupling coefficient k(15) and piezoelectric stress constant e(15) when compared to the piezoceramic fibre properties. Therefore, the main objective of this work is to perform a parametric analysis in which the effect of the variations of fibre volume fraction, Epoxy elastic modulus, electrode thickness and active layer thickness on the MFC effective material properties is evaluated. Results indicate that an effective d(15) MFC should use relatively thick fibres having relatively high shear modulus and relatively stiff epoxy filler. On the other hand, the electrode thickness does not affect significantly the MFC performance.

Parametric analysis of effective material properties of thickness-shear piezoelectric macro-fibre composites

A previous study on the characterization of effective material properties of a d15 thickness-shear piezoelectric Macro-Fibre Composite (MFC) made of seven layers (Kapton, Acrylic, Electrode, Piezoceramic Fibre and Epoxy Composite, Electrode, Acrylic, Kapton) using a finite element homogenization method has shown that the packaging reduces significantly the shear stiffness of the piezoceramic material and, thus, leads to significantly smaller effective electromechanical coupling coefficient k15 and piezoelectric stress constant e15 when compared to the piezoceramic fibre properties. Therefore, the main objective of this work is to perform a parametric analysis in which the effect of the variations of fibre volume fraction, Epoxy elastic modulus, electrode thickness and active layer thickness on the MFC effective material properties is evaluated. Results indicate that an effective d15 MFC should use relatively thick fibres having relatively high shear modulus and relatively stiff epoxy filler. On the other hand, the electrode thickness does not affect significantly the MFC performance.

A bridging transition technique for the combination of meshfree method with finite element method in 2D solids and structures

For certain continuum problems, it is desirable and beneficial to combine two different methods together in order to exploit their advantages while evading their disadvantages. In this paper, a bridging transition algorithm is developed for the combination of the meshfree method (MM) with the finite element method (FEM). In this coupled method, the meshfree method is used in the sub-domain where the MM is required to obtain high accuracy, and the finite element method is employed in other sub-domains where FEM is required to improve the computational efficiency. The MM domain and the FEM domain are connected by a transition (bridging) region. A modified variational formulation and the Lagrange multiplier method are used to ensure the compatibility of displacements and their gradients. To improve the computational efficiency and reduce the meshing cost in the transition region, regularly distributed transition particles, which are independent of either the meshfree nodes or the FE nodes, can be inserted into the transition region. The newly developed coupled method is applied to the stress analysis of 2D solids and structures in order to investigate its’ performance and study parameters. Numerical results show that the present coupled method is convergent, accurate and stable. The coupled method has a promising potential for practical applications, because it can take advantages of both the meshfree method and FEM when overcome their shortcomings.

A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media

We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.