A compatible and complete six-noded element to model singularity

The shape functions of a six-noded triangular element are developed to model power type singularities which satisfy all the convergence criteria—the rigid body mode, the interelement continuity and the constant strain condition. Hence this provides a unique tool to model power type singularities under mechanical and thermal loads. Three case studies are presented. The first case study deals with the comparison of the present element with the existing singular elements. The convergence studies are done for this case study by refining the mesh and also by increasing the order of integration. The second and the third case studies deal with real life problems, namely, the analysis of a cracked bimaterial strip and the analysis of a power plant nozzle with a kinked crack under mechanical and thermal loads. These case studies show the usefulness of the element.     

A finite element for 3-D prestressed cablenets

A finite element method is presented for the analysis of prestressed cablenets. The method is based on representing the prestressed cablenet as a series of finite length curved elements. The large displacement formulation used, enables the evaluation of the static and dynamic response of 3-D cablenets. The development is general and the mathematical basis is explained at length. It is shown by means of comparison functions that for absolute continuity at nodes, a cubic displacement field is sufficient for the prediction of the first frequency of shallow nets. For globally deep networks the accuracy can be increased by employing a quintic displacement field for the normal component of displacement. The application of the proposed model to cable structures of shallow and also of deep global geometry, is presented. A variety of edge boundary shapes are employed in order to illustrate the versatility of the large displacement formulation. In all the example problems studied, gravity load has been taken as the initial load condition in calculating the equilibrium configuration. The stiffness and consistent mass matrices associated with the equation of motion are derived using Hamilton's variational principle.     

A new 3-D finite element model to evaluate added mass for analysis of fluid-structure interaction problems

The paper presents the results of investigations conducted to evaluate the added mass to represent fluid-structure interaction effects in vibration/dynamic analysis of floating bodies such as ship hulls. While the structural plating is idealized by 9-noded plate/shell finite elements, the fluid domain is modelled by 20-noded/21-noded 3-D finite elements in the investigations conducted. A new 8-noded element has been developed to model the interface between the structure and the fluid. An efficient computational methodology has been used for computation of added mass. The finite element models are validated by comparing the results with those given by analytical solution for a submerged sphere. The efficacy of the finite element model is demonstrated through convergence of the results obtained for a floating barge problem. A better convergence rate and distribution of added mass in three orthogonal directions have been obtained.     

A study of finite size effects on cracked 2-D piezoelectric media using extended finite element method

The extended finite element method is applied on the two-dimensional (2-D) finite piezoelectric media weakened by a crack. The fourfold standard enrichment functions are taken in conjugation with the interaction integral to evaluate the intensity factors. Four sequence of analysis, namely crack–mesh alignment, aspect ratio, mesh with local refinement and domain independency is done on the center and edge crack problems. These four analyses when combined together give an optimum result to study the finite specimen. It is observed that for smaller values of strip width to crack length ratio the finiteness of the specimen size affects the intensity factors.     

2-D multiplane finite element technique for solving a class of 3-D problems

A finite element technique, for efficient solution of a class of 3-D elasticity problems, is presented. In this method, standard 2-D finite elements are used along with a ‘connector’ element. An element, previously used to model material interfaces, is shown to provide the properties for use as a ‘connector’ element, if input variables are redefined. The accuracy of the technique is illustrated with a sample solution.     

Hyperbolic constitutive model to study cast iron pipes in 3-D nonlinear finite element analyses

Cast iron (CI) pipes were widely installed as water mains and service connections in the last century and still large numbers of CI pipes remain in service. However, many CI pipes are becoming aged and severely corroded, causing frequent pipe leaks and breaks. To better understand the failure mechanism of CI pipes, this paper provides an efficient numerical approach to analyse the behaviour of CI pipes under various loading conditions. The numerical investigation was realised by implementing a hyperbolic constitutive model (a simplified nonlinear stress-strain analysis) for CI materials into finite element analysis (FEA) in ABAQUS. Three-dimensional (3-D) FEAs were carried out for a series of uniaxial tensile and compressive tests, 3-point beam bending tests and ring bending tests on various CI pipe coupons. The stress-strain characteristics and load-deflection responses obtained from these numerical examples were validated by experimental results. The numerical results obtained from the proposed method are in good agreement with the measured data, which indicates that the mechanical performance of deteriorated CI pipes can be adequately modelled using the relatively simple nonlinear constitutive model implemented in 3-D FEA. As nonlinear behaviour has proven to be intrinsic to the widely used CI pipes, it is expected that the proposed 3-D FEA modelling technique will be of importance to the evaluation of the mechanical performance of CI pipes and, possibly, other CI structures.     

Stiffness derivative finite element technique to determine nodal weight functions with singularity elements

The use of the stiffness derivative technique coupled with “quarter-point” singular crack-tip elements permits very efficient finite element determination of both stress intensity factors and nodal weight functions. Two-dimensional results are presented in this paper to demonstrate that accurate stress intensity factors and nodal weight functions can be obtained from relatively coarse mesh models by coupling the stiffness derivative technique with singular elements.The principle of linear superposition implies that the calculation of stress intensity factors and nodal weight functions with crack-face loading, σ($\text{r}{}_{\mathrm{s}}$), is equivalent to loading the cracked body with remote loads, which produces σ($\text{r}{}_{\mathrm{s}}$) on the prospective crack face in the absence of crack. The verification of this equivalency is made numerically, using the virtual crack extension technique. Load independent nodal weight functions for two-dimensional crack geometry is demonstrated on various remote and crack-face loading conditions. The efficienct calculation of stress intensity factors with the use of the “uncracked” stress field and the crack-face nodal weight functions is also illustrated.In order to facilitate the utilization of the discretized crack-face nodal weight functions, an approach was developed for two-dimensional crack problems. Approximations of the crack-face nodal weight functions as a function of distance, ($\text{r}{}_{\mathrm{s}}$), from crack-tip has been sucessfully demonstrated by the following equation: $\text{h(a, r}{}_{\mathrm{s}}\text{,) =}\text{A(a)}\text{√r}{}_{\mathrm{s}}\text{+ B(a) + C(a)√r}{}_{\mathrm{s}}\text{+ D(a)r}{}_{\mathrm{s}}$.Coefficients $\text{A(a)}$, $\text{B(a)}$, $\text{C(a)}$ and $\text{D(a)}$, which are functions of crack length ($\text{a}$), can be obtained by least-squares fitting procedures. The crack-face nodal weight functions for a new crack geometry can be approximated using cubic spline interpolation of the coefficients $\text{A, B, C}$ and $\text{D}$ of varying crack lengths. This approach, demonstrated on the calculation of stress intensity factors for single edge crack geometry resulted in total loss of accuracy of less than 1%.     

Complementary 2-D finite element procedures for the magnetic field analysis using a vector hysteresis model

The main purpose of this paper is to incorporate a refined hysteresis model, viz., a vector Preisach model, in 2-D magnetic field computations. Two complementary formulations, based either on the scalar or on the vector potential, are considered. The governing Maxwell equations are rewritten in a suitable way, that allows to take into account the proper magnetic material parameters and, moreover, to pass to a variational formulation. The variational problems are solved numerically by a Finite Element approximation, using a quadratic mesh, followed by a time discretization method based upon a modified Cranck–Nicholson algorithm. Finally, the effectiveness of the presented mathematical tools have been confirmed by several numerical experiments, comparing the complementarity of the two procedures. © 1998 John Wiley & Sons, Ltd.     

Mechanical properties of functionally graded 2-D cellular structures: A finite element simulation

Functionally graded cellular structures such as bio-inspired functionally graded materials for manufacturing implants or bone replacement, are a class of materials with low densities and novel physical, mechanical, thermal, electrical and acoustic properties. A gradual increase in cell size distribution, can impart many improved properties which may not be achieved by having a uniform cellular structure.The material properties of functionally graded cellular structures as a function of density gradient have not been previously addressed within the literature. In this study, the finite element method is used to investigate the compressive uniaxial and biaxial behavior of functionally graded Voronoi structures. Furthermore, the effect of missing cell walls on its overall mechanical (elastic, plastic, and creep) properties is investigated.The finite element analysis showed that the overall effective elastic modulus and yield strength of structures increased by increasing the density gradient. However, the overall elastic modulus of functionally graded structures was more sensitive to density gradient than the overall yield strength. The study also showed that the functionally graded structures with different density gradient had similar sensitivity to random missing cell walls. Creep analysis suggested that the structures with higher density gradient had lower steady-state creep rate compared to that of structures with lower density gradient.     

A finite element model for thin-walled members

Thin-walled members subject to generalized loading may be modelled by using a finite element approach with conventional stress and strain parameters. A solution method for a class of problems that would use these elements is described. A numberical example of an elastic beam is given.     

A finite element model of skeletal muscles

The present paper surveys recent developments in constitutive and computational modelling of skeletal muscles, concerning mainly the generalization to two- and three-dimensional (2D, 3D) continuum deformation analysis of typical one-dimensional (1D) Hill-type muscle models. Extending our previous work in the field and recent contributions by other authors, we describe a constitutive model for skeletal muscles that incorporates all the features of the 3 typical elements (parallel elastic, series elastic and contractile elements) in Hill's muscle model. In particular the proposed incompressible transversely isotropic model incorporates: a multiplicative split of the fibre stretch into contractile and (series) elastic stretches; the possibility of energy storage in the series elastic element; the dependence of the contractile stress on the strain rate; the governing equation of activation dynamics, so that general histories of neural stimulation may be taken as input data. The resulting 2D or 3D constitutive equations are implemented as user subroutines in the large deformation finite element software package ABAQUS. Simple numerical tests are presented and discussed, as well as an example that involves passive or active deformations of a pelvic floor muscle using shell finite elements.     

A finite element model of skeletal muscles

The present paper surveys recent developments in constitutive and computational modelling of skeletal muscles, concerning mainly the generalization to two- and three-dimensional (2D, 3D) continuum deformation analysis of typical one-dimensional (1D) Hill-type muscle models. Extending our previous work in the field and recent contributions by other authors, we describe a constitutive model for skeletal muscles that incorporates all the features of the 3 typical elements (parallel elastic, series elastic and contractile elements) in Hill's muscle model. In particular the proposed incompressible transversely isotropic model incorporates: a multiplicative split of the fibre stretch into contractile and (series) elastic stretches; the possibility of energy storage in the series elastic element; the dependence of the contractile stress on the strain rate; the governing equation of activation dynamics, so that general histories of neural stimulation may be taken as input data. The resulting 2D or 3D constitutive equations are implemented as user subroutines in the large deformation finite element software package ABAQUS. Simple numerical tests are presented and discussed, as well as an example that involves passive or active deformations of a pelvic floor muscle using shell finite elements.     

A finite element model for Mindlin plates

In the general framework of Reissner-Mindlin theory, a plate model based on certain potential functions is discussed, together with its mechanical interpretation. A finite element implementation is also described and numerical results are reported.     

A hybrid finite element model for multilayered plates

We present a finite element model for multilayered plates, based on a primal-hybrid variational formulation. Namely, each layer is analyzed as it were a lonely structure, and the displacement continuity is imposed from one layer to the other by means of Lagrange multipliers. Then, a Mindlin-like displacement field is assumed for any layer; the resulting continuous problem is proven to be well-posed under rather general hypotheses. Finally, a finite element model is deduced, using a very simple scheme (piecewise linear approximation for the displacement components and piecewise constant Lagrange multipliers). The numerical results assess the good performance of the proposed model.     

A finite element model for single-sided crack patchings

A finite element model is established for analyzing the behavior of cracked plates which are repaired with a single-sided patch. The formulation is based on the Reissner-Mindlin plate theory with an assumed variation of the transverse shear and normal stresses through the thickness of the cracked -plate and patch. The generalized stress-strain relations relating the transverse shear stress resultants and the adhesive stresses to the displacements of the plate and patch are established by using a variational principle. By means of the finite element model presented herein, single-sided crack patching problems can be solved with a reasonable estimate of the adhesive stresses and the stress intensity factor. Numerical examples are provided to illustrate the effects of the patch size on the stress intensity factor in the cracked plate and the stress distribution in the adhesive layer, and compared with results from the previous analysis.     

A finite element model for shape memory behavior

This paper deals with a finite element implementation concerning the shape memory behavior. Shape memory behavior is usually driven by temperature changes. This model allows the simulation of problems integrating complex mechanical loading effects under random temperature variations. According to the relationship between stress and strain, the shape fixation during cooling phases and the memory effect during heating phase are modelised through a hereditary behavior needing incremental formulation developments. The step by step process introduces an additional fixed stress. Simulations request, for complex geometries including boundary conditions, a finite element approach. Thermodynamic developments are presented in order to define energetic balance and dissipations. In this paper, we propose to generalize this dependence of elastic modulus variations. A formulation for random mechanical loading and temperature variations is proposed. An experimental validation is proposed about shape memory alloy polymer DP5.     

A finite element model for liquid phase electroepitaxy

A finite element numerical simulation model for the liquid phase electroepitaxial growth process of gallium arsenide is presented. The basic equations obtained from the fundamental principles of electrodynamics of continua, the constitutive equations for the liquid and solid phases derived from a rational thermodynamic theory, and the associated interface and boundary conditions are presented for a two-dimensional axisymmetric growth cell configuration. The field equations are solved numerically by an adaptive finite element procedure. The effect of moving interfaces is taken into account. Numerical simulations are carried out for different convection levels by changing the value of the gravitational constant. Results show that convection has significant effect on the growth process under normal gravity conditions and results in thickness non-uniformity of the grown layers. The thickness non-uniformity leads to curved interfaces of growth and dissolution, which enhance convection.     

A linear finite element model to predict processing-induced distortion in FRP laminates

Manufacturing processes for laminated composites often produce parts whose dimensions do not match the mold from which they were made. This distortion is commonly referred to as ‘spring-in’. The amount of spring-in can depend on many factors including the manufacturing process (cure temperature, resin bleed, and applied pressure), the part (geometry, material, thickness, cure shrinkage, thermal expansion and layup sequence), and the tool (surface, thickness and thermal expansion). Much of the current work devoted to spring-in relies on extensive resin characterization. While this approach has been reasonably successful, it does little to assist the designer using material systems that have not been fully characterized (which is not always possible or feasible). This study considers the ability of a linear elastic finite element model to describe and quantify many of the factors contributing to spring-in. The aim of this study is to show that spring-in can be accurately predicted without a complete resin characterization. Numerical predictions based on relatively simple mechanical tests were observed to compare favorably with experimental measurements. Spring-in was dominated by thickness shrinkage, which contributed approximately 3/4 of the measured distortion. The mold stretching contribution diminished with thickness and was negligible for parts thicker than 2.5 mm (0.1 in.). While the material system at hand did not exhibit a fiber volume fraction gradient, its effects were included in the formulation of the model. For materials that have reported a gradient, it was found to account for approximately 10% of the part spring-in.     

A finite element model for nonlinear shells of revolution

A finite element model for symmetrically loaded shells of revolution is described. The nonlinear geometric effects are accounted for by incrementing loads and iterating for equilibrium. The iteration process also allows for nonlinear materials. The shell model accounts for large strains, large rotations and shear deformation. Three example problems demonstrate the ability of this model to solve linear problems. Also, three example problems demonstrate the versatility and accuracy of this model for nonlinear problems. These nonlinear example problems are an axially loaded cylinder and an internally pressurized spherical shell that have large membrane strains, and a cylinder that deforms into a spherical shape, having large rotations.