R. Palaninathan

CURVED BEAM ELEMENT STIFFNESS MATRIX FORMULATION

Abstract Stiffness matrix of order 12 × 12, for a curved beam element has been formulated involving all the forces together, using Castiglianos theorem. Effects of transverse shear forces and tangential thrust are also taken into account. In earlier works, stiffness submatrices for the two uncoupled systems of forces are formulated independently and then they are combined to give the overall 12 × 12 matrix. A program subroutine, NEWCBM for the stiffness matrix formulation of curved beams has been written in FORTRAN which can be added to the element library of general purpose computer programs like SAP-IV and its improved versions. Example problems have been worked to check the accuracy of this formulation.

Free vibration of skew laminates

Abstract A general high precision triangular plate bending finite element has been extended to the free vibration analysis of laminated skew plates by deriving the consistent mass matrix in explicit form. The boundary conditions on the skew edges are imposed through the transformed element matrices. The accuracy of the present formulation has been verified against literature values. The fundamental frequencies are obtained for simply supported and clamped antisymmetric angle-ply skew laminates. In this analysis, the effects of skew angle, fibre orientation angle, number of layers and stacking sequence on the fundamental frequency have been studied. The frequencies are found to increase with skew angle. Also, the skew angle is seen to have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate.

Finite element analysis of laminated shells with exact through-thickness integration

Abstract The conventional degenerated shell element which involves numerical integration in three dimensions becomes inefficient when applied to multilayered shells. For the computational efficiency, layered element based on the explicit integration through thickness assumes importance. The explicit integration becomes possible due to the assumption concerning the variation of inverse Jacobian through the thickness. Depending on the level of approximation, whether linearly varying or constant Jacobian inverse along the thickness, three models are discussed. Examples of stress analysis and classical buckling are considered for the comparative studies relating to the computational efficiency and numerical accuracy. The model, which assumes linear variation of Jacobian inverse through thickness with further approximations is seen to be the best from numerical accuracy and computational efficiency points of view.

Buckling of laminated skew plates

A general high precision triangular plate bending finite element has been extended to the buckling analysis of laminated skew plates. This procedure involves development of the transformation matrix between global and local degrees of freedom for nodes lying on the skew edges and suitable transformation of the element matrices. The accuracy of the present formulation has been verified against literature values. New results are obtained for antisymmetric angle-ply and cross-ply laminated skew plates. In this analysis, the critical buckling loads for different skew angles with various lamination parameters, such as number of layers, fibre orientation angle, different boundary (simply supported, clamped) and loading (uniaxial, biaxial) conditions, have been presented.

Modeling of Mechanical Ablation in Thermal Protection Systems

An integrated thermomechanical modeling of response of low-temperature ablative thermal protection system under thermal loading encountered by reentry vehicles is presented. Of the three thermal protection mechanisms, thermal, chemical, and mechanical ablations, only the latter is assumed to influence the recession in the presence of aerodynamic surface shear for materials with low shear strength at higher temperatures. A model for the mechanical ablation (erosion) is presented that is based on the matching point scheme. The degenerated doubly curved shell element is employed in the modeling. This enables consideration of the general type of aerodynamic loads, distributed and varying with surface and time coordinates, which differs from the earlier studies reported in the open literature. The finite element method uses polynomial approximation to represent the nonlinear through-thickness temperature profile and explicit-through-thickness integration in the computation of element matrices. This brings in computational efficiency without loss of numerical accuracy, particularly in the context of multilayered construction. No attempt is made to compute the incident heat flux and other aerodynamic loads. Numerical examples are presented for specified loads to bring out the influences of material properties and heating rates on surface recession and are based mostly on assumed material properties.

Experimental investigations on buckling of cylindrical shells under axial compression and transverse shear

This paper presents experimental studies on buckling of cylindrical shell models under axial and transverse shear loads. Tests are carried out using an experimental facility specially designed, fabricated and installed, with provision forin-situ measurement of the initial geometric imperfections. The shell models are made by rolling and seam welding process and hence are expected to have imperfections more or less of a kind similar to that of real shell structures. The present work thus differs from most of the earlier investigations. The measured maximum imperfections δmax are of the order of ±3t (t = thickness). The buckling loads obtained experimentally are compared with the numerical buckling values obtained through finite element method (FEM). In the case of axial buckling, the imperfect geometry is obtained in four ways and in the case of transverse shear buckling, the FE modelling of imperfect geometry is done in two ways. The initial geometric imperfections affect the load carrying capacity. The load reduction is considerable in the case of axial compression and is marginal in the case of transverse shear buckling. Comparisons between experimental buckling loads under axial compression, reveal that the extent of imperfection, rather than its maximum value, in a specimen influences the failure load. Buckling tests under transverse shear are conducted with and without axial constraints. While differences in experimental loads are seen to exist between the two conditions, the numerical values are almost equal. The buckling modes are different, and the experimentally observed and numerically predicted values are in complete disagreement.

Explicit through-thickness integration schemes for geometric nonlinear analysis of laminated composite shells

Degenerated shell elements were found to be attractive in solving homogeneous shell problems. Direct extension of the same to layered shells becomes computationally inefficient as, in the computation of element matrices, 3-D numerical integration in each layer and summation over the layers have to be carried out. In order to make the formulation efficient, explicit through-thickness schemes have been devised for linear problems. The present paper deals with the extension of the same to geometric nonlinear problems with options of small and large rotations. The explicit through-thickness integration becomes possible due to the assumption on the variation of inverse Jacobian through the thickness. Depending on the assumptions, three different schemes under large and small rotation cases have been presented and their relative numerical accuracy and computational efficiency have been evaluated. It has been observed that there is no sacrifice on the numerical accuracy due to the assumptions leading to the explicit through-thickness integration, but at the same time, there is considerable saving in the computational time. The computational efficiency improves as the number of layers in the laminate increases. The small rotation formulation with the assumption of linear variation of Jacobian inverse across the thickness and based on further approximation regarding certain submatrices is seen to be computationally efficient, as applied to geometric nonlinear layered shell problems.

Thermal analysis of piston casting using 3-D finite element method

Abstract This paper presents a finite element modelling of metal solidification, applied to an aluminum–silicon alloy piston casting. Earlier studies on solidification have been mostly confined to one- and two-dimensional problems whereas the present one deals with 3-D castings. It is assumed that the heat transfer within the melt is by conduction and that from the melt/casting to the mold is by the interfacial heat transfer process. The air gap formed between the casting and the mold at interface affects the heat transfer rate. A finite element formulation for the heat transfer through the air gap is presented for the 3-D problems. The same is applied to the specific case of piston solidification. Temperature profiles at different time steps are presented. The time taken for completion of solidification with respect to the process parameters are discussed.

Impact experiments on shallow spherical shells

Experimental and theoretical results on the dynamic response of shallow spherical shells subjected to concentrated impact forces at the apex are presented in this work. Theoretical transient response results for half sine impact forces with several pulse durations have been obtained on the basis of improved shell theory which includes transverse shear and rotatory inertia effects. With a view to checking the acceptability of the analytical results, experiments were conducted on four shallow spherical shell models. For several pulse durations, covering short and long pulse ranges, the shells were subjected to axisymmetric and asymmetric impact loads at the apex. The applied force and the resulting deformations were recorded for each of the loadings. Experimental results agree quite well with analytical predictions, and they clearly illustrate the effect of pulse duration as well as other dynamical aspects.

Modeling of Liquid Metal Infiltration of Porous Fiber Preform During Squeeze Casting

The present work adopts a new approach to the analytical modeling of infiltration of porous fiber preforms by liquid metal in the squeeze casting of metal matrix composites, with the assumption that the process is adiabatic and that the flow is unidirectional. Fluid dynamics is described on the basis of Darcys law, while separate equations are derived to explain the thermal behavior of the liquid metal and the fiber, assuming that the thermal interactions between the two are interfacial. Unlike earlier models, this approach does not consider the thermal behavior of a “composite,” but instead studies the behavior of the liquid metal and the fiber preform separately. In addition to the conventional application of heat balance techniques and development of partial differential equations involving temperatures, this work introduces supplementary conditions for temperature calculations, specifically at the entry and front points during infiltration. Differential equations are solved by a method of finite differences, and the problem of additional unknowns (preform temperature) at the infiltration front position is overcome using the “virtual point” concept. Simple expressions are derived for the calculation of process parameters like total time for complete infiltration and time for solidification, on the basis of which the occurrence of complete infiltration is predicted. A novel attempt in generating the profiles of the preform and liquid temperatures at specific instants during infiltration has also been made. The relative influence of the liquid superheat temperature, the preform preheat temperature, and the squeeze pressure on the infiltration mechanism is analyzed by studying the infiltration characteristics for various squeeze conditions.