Finite element analysis of curved anisotropic laminated hollow bars

Curved hollow bars of laminated anisotropic construction are used as structural members in many industries. They are used in order to save weight without loss of stiffness in comparison with solid sections. In this paper are presented the details of the development of the stiffness matrices of laminated anisotropic curved hollow bars under line member assumptions for two typical sections, circular and square. They are 16dof elements which make use of one-dimensional first-order Hermite interpolation polynomials for the description of assumed displacement state. Problems for which analytical or other solutions are available are first solved using these elements. Good agreement was found between the results. In order to show the capability of the element, application is made to carbon fibre reinforced plastic layered anisotropic curved hollow bars.

Finite element analysis of laminated anisotropic beams of bimodulus materials

This paper presents finite element analysis of laminated anisotropic beams of bimodulus materials. The finite element has 16 d.o.f. and uses the displacement field in terms of first order Hermite interpolation polynomials. As the neutral axis position may change from point to point along the length of the beam, an iterative procedure is employed to determine the location of zero strain points along the length. Using this element some problems of laminated beams of bimodulus materials are solved for concentrated loads/moments perpendicular and parallel to the layering planes as well as combined loads.

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

New rational interpolation functions for finite element analysis of rotating beams

A rotating beam finite element in which the interpolating shape functions are obtained by satisfying the governing static homogenous differential equation of Euler–Bernoulli rotating beams is developed in this work. The shape functions turn out to be rational functions which also depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. These rational functions yield the Hermite cubic when rotation speed becomes zero. The new element is applied for static and dynamic analysis of rotating beams. In the static case, a cantilever beam having a tip load is considered, with a radially varying axial force. It is found that this new element gives a very good approximation of the tip deflection to the analytical series solution value, as compared to the classical finite element given by the Hermite cubic shape functions. In the dynamic analysis, the new element is applied for uniform, and tapered rotating beams with cantilever and hinged boundary conditions to determine the natural frequencies, and the results compare very well with the published results given in the literature.

A finite element analysis of quasistatic crack growth in a pressure sensitive constrained ductile layer

Polymeric adhesive layers are employed for bonding two components in a wide variety of technological applications, It has been observed that, unlike in metals, the yield behavior of polymers is affected by the state of hydrostatic stress. In this work, the effect of pressure sensitivity of yielding and layer thickness on quasistatic interfacial crack growth in a ductile adhesive layer is investigated. To this end, finite deformation, finite element analyses of a cracked sandwiched layer are carried out under plane strain, small-scale yielding conditions for a wide range of mode mixities. The Drucker-Prager constitutive equations are employed to represent the behavior of the layer. Crack propagation is simulated through a cohesive zone model, in which the interface is assumed to follow a prescribed traction-separation law. The results show that for a given mode mixity, the steady state Fracture toughness [K](ss) is enhanced as the degree of pressure sensitivity increases. Further, for a given level of pressure sensitivity, [K](ss) increases steeply as mode Il loading is approached. (C) 2000 Elsevier Science Ltd. All rights reserved.

A finite element analysis of dynamic fracture initiation by ductile failure mechanisms in a 4340 steel

In some recent dropweight impact experiments [5] with pre-notched bend specimens of 4340 steel, it was observed that considerable crack tunneling occurred in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments happened because of shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. In this paper, the experiments of [5] (corresponding to 5 m/s impact speed) are analyzed using a plane strain, dynamic finite element procedure. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed. The time at which incipient failure was observed near the notch tip in this computation, and the value of the dynamic J-integral, J d, at this time, compare reasonably well with experiments. This investigation shows that J-controlled stress and deformation fields are established near the notch tip whenever J d , increases with time. Also, it is found that the evolution of micro-mechanical quantities near the notch root can be correlated with the time variation of J d .The strain rate and the adiabatic temperature rise experienced at the notch root are examined. Finally, spatial variations of stresses and deformations are analyzed in detail.

Analysis of reflection characteristics of a normal incidence plane wave on resonant sound absorbers: A finite element approach

Resonant sound absorbers are used widely as anechoic coatings in underwater applications. In this paper a finite element scheme based on the Galerkin technique is used to analyze the reflection characteristics of the resonant absorber when insonified by a normal incidence plane wave. A waveguide theory coupled with an impedance matching condition in the fluid is used to model the problem. It is shown in this paper that the fluid medium encompassing the absorber can be modeled as an elastic medium with equivalent Lamé constants. Quarter symmetry conditions within the periodic unit cell are exploited. The finite element results are compared with analytical results, and with results published elsewhere in the literature. It is shown in the process that meshing of the fluid domain can be obviated if the transmission coefficients or reflection coefficients only are desired as is often the case. Finally, some design curves for thin resonant absorbers with water closure are presented in this paper.

Analysis of the evanescent field coupling between a fiber and a planar waveguide using the explicit finite difference method with a nonuniform mesh (Journal Paper)

We investigate an optical waveguide system consisting of an unclad fiber core suspended at a constant distance parallel to the surface of a planar waveguide. The coupling and propagation of light in the combined system is studied using the three-dimensional explicit finite difference beam propagation method with a nonuniform mesh configuration. The power loss in the fiber and the field distribution in the waveguide are studied as a function of various parameters, such as index changes, index profile, and propagation distance, for the combined system.

Study of Layering Procedures in Finite-Element Analysis of RC Flexural and Torsional Elements

A new postcracking formulation for concrete, along with both implicit and explicit layering procedures, is used in the analysis of reinforced-concrete (RC) flexural and torsional elements. The postcracking formulation accounts for tension stiffening in concrete along the rebar directions, compression softening in cracked concrete based on either stresses or strains, and aggregate interlock based on crack-confining normal stresses. Transverse shear stresses computed using the layering procedures are included in material model considerations that permit the development of inclined cracks through the RC cross section. Examples of a beam analyzed by both the layering techniques, a torsional element, and a column-slab connection region analyzed by the implicit layering procedure are presented here. The study highlights the primary advantages and disadvantages of each layering approach, identifying the class of problems where the application of either procedure is more suitable.

Physics based basis function for vibration analysis of high speed rotating beams

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

A new beam finite element for the analysis of functionally graded materials

A new beam element is developed to study the thermoelastic behavior of functionally graded beam structures. The element is based on the first-order shear deformation theory and it accounts for varying elastic and thermal properties along its thickness. The exact solution of static part of the governing differential equations is used to construct interpolating polynomials for the element formulation. Consequently, the stiffness matrix has super-convergent property and the element is free of shear locking. Both exponential and power-law variations of material property distribution are used to examine different stress variations. Static, free vibration and wave propagation problems are considered to highlight the behavioral difference of functionally graded material beam with pure metal or pure ceramic beams. (C) 2003 Elsevier Science Ltd. All rights reserved.

Reconstructing Solid Model from 2D Scanned Images of Biological Organs for Finite Element Simulation

This work presents a methodology to reconstruct 3D biological organs from image sequences or other scan data using readily available free softwares with the final goal of using the organs (3D solids) for finite element analysis. The methodology deals with issues such as segmentation, conversion to polygonal surface meshes, and finally conversion of these meshes to 3D solids. The user is able to control the detail or the level of complexity of the solid constructed. The methodology is illustrated using 3D reconstruction of a porcine liver as an example. Finally, the reconstructed liver is imported into the commercial software ANSYS, and together with a cyst inside the liver, a nonlinear analysis performed. The results confirm that the methodology can be used for obtaining 3D geometry of biological organs. The results also demonstrate that the geometry obtained by following this methodology can be used for the nonlinear finite element analysis of organs. The methodology (or the procedure) would be of use in surgery planning and surgery simulation since both of these extensively use finite elements for numerical simulations and it is better if these simulations are carried out on patient specific organ geometries. Instead of following the present methodology, it would cost a lot to buy a commercial software which can reconstruct 3D biological organs from scanned image sequences.