Thermal instability in a three-dimensional rigid container with prescribed heat flux at lower boundary

The Bénard–Marangoni convection is studied in a three-dimensional container with thermally insulated lateral walls and prescribed heat flux at lower boundary. The upper surface of the incompressible, viscous fluid is assumed to be flat with temperature dependent surface tension. A Galerkin–Tau method with odd and even trial functions satisfying all the essential boundary conditions except the natural boundary conditions at the free surface has been used to solve the problem. The critical Marangoni and Rayleigh numbers are determined for the onset of steady convection as a function of aspect ratios x0 and y0 for the cases of Bénard–Marangoni, pure Marangoni and pure Bénard convections. It is observed that critical parameters are decreasing with an increase in aspect ratios. The flow structures corresponding to the values of the critical parameters are presented in all the cases. It is observed that the critical parameters are higher for case with heat flux prescribed than those corresponding to the case with prescribed temperature. The critical Marangoni number for pure Marangoni convection is higher than critical Rayleigh number corresponding to pure Bénard convection for a given aspect ratio whereas the reverse was observed for two-dimensional infinite layer.

New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method

A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.

Comparative study on damage identification from lso-Eigen-Value-Change contours and smeared damage model

The paper proposes two methodologies for damage identification from measured natural frequencies of a contiguously damaged reinforced concrete beam, idealised with distributed damage model. The first method identifies damage from Iso-Eigen-Value-Change contours, plotted between pairs of different frequencies. The performance of the method is checked for a wide variation of damage positions and extents. The method is also extended to a discrete structure in the form of a five-storied shear building and the simplicity of the method is demonstrated. The second method is through smeared damage model, where the damage is assumed constant for different segments of the beam and the lengths and centres of these segments are the known inputs. First-order perturbation method is used to derive the relevant expressions. Both these methods are based on distributed damage models and have been checked with experimental program on simply supported reinforced concrete beams, subjected to different stages of symmetric and un-symmetric damages. The results of the experiments are encouraging and show that both the methods can be adopted together in a damage identification scenario.

Finite element analysis of shear critical prestressed SFRC beams

This study reports the details of the finite element analysis of eleven shear critical partially prestressed concrete T-beams having steel fibers over partial or full depth. Prestressed concrete T-beams having a shear span to depth ratio of 2.65 and 1.59 and failing in the shear have been analyzed Using 'ANSYS'. The 'ANSYS' model accounts for the nonlinear phenomenon, such as, bond-slip of longitudinal reinforcements, post-cracking tensile stiffness of the concrete, stress transfer across the cracked blocks of the concrete and load sustenance through the bridging of steel fibers at crack interlace. The concrete is modeled using 'SOLID65'-eight-node brick element, which is capable Of simulating the cracking and crushing behavior of brittle materials. The reinforcements such as deformed bars, prestressing wires and steel fibers have been modeled discretely Using 'LINK8' - 3D spar element. The slip between the reinforcement (rebar, fibers) and the concrete has been modeled using a 'COMBIN39'-non-linear spring element connecting the nodes of the 'LINK8' element representing the reinforcement and nodes of the 'SOLID65' elements representing the concrete. The 'ANSYS' model correctly predicted the diagonal tension failure and shear compression failure of prestressed concrete beams observed in the experiment. I-lie capability of the model to capture the critical crack regions, loads and deflections for various types Of shear failures ill prestressed concrete beam has been illustrated.

A dragonfly inspired flapping wing actuated by electro active polymers

An energy-based variational approach is used for structural dynamic modeling of the IPMC (Ionic Polymer Metal Composites) flapping wing. Dynamic characteristics of the wing are analyzed using numerical simulations. Starting with the initial design, critical parameters which have influence on the performance of the wing are identified through parametric studies. An optimization study is performed to obtain improved flapping actuation of the IPMC wing. It is shown that the optimization algorithm leads to a flapping wing with dimensions similar to the dragonfly Aeshna Multicolor wing. An unsteady aerodynamic model based on modified strip theory is used to obtain the aerodynamic forces. It is found that the IPMC wing generates sufficient lift to support its own weight and carry a small payload. It is therefore a potential candidate for flapping wing of micro air vehicles.

New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

Vibration and Stability of Fluid Conveying Pipes with Stochastic Parameters

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is-first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

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.

Automatic decomposition of unstructured meshes employing genetic algorithms for parallel FEM computations

Parallel execution of computational mechanics codes requires efficient mesh-partitioning techniques. These mesh-partitioning techniques divide the mesh into specified number of submeshes of approximately the same size and at the same time, minimise the interface nodes of the submeshes. This paper describes a new mesh partitioning technique, employing Genetic Algorithms. The proposed algorithm operates on the deduced graph (dual or nodal graph) of the given finite element mesh rather than directly on the mesh itself. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialise an optimisation of the graph partition problem. In practice, hierarchy of (usually more than two) graphs are used to obtain the final graph partition. The proposed partitioning algorithm is applied to graphs derived from unstructured finite element meshes describing practical engineering problems and also several example graphs related to finite element meshes given in the literature. The test results indicate that the proposed GA based graph partitioning algorithm generates high quality partitions and are superior to spectral and multilevel graph partitioning algorithms.

Structural vibration control using resistively shunted piezoceramics

Application of piezoceramic materials in actuation and sensing of vibration is of current interest. Potential and more popular applications of piezoceramics are probably in the field of active vibration control. However, the objective of this work is to investigate the effect of shunted piezoceramics as passive vibration control devices when bonded to a host structure. Resistive shunting of a piezoceramic bonded to a cantilevered duralumin beam has been investigated. The piezoceramic is connected in parallel to an electrical network comprising of resistors and inductors. The piezoceramic is a capacitor that stores and discharges electrical energy that is transformed from the mechanical motion of the structure to which it is bonded. A resistor across the piezoceramic would be termed as a resistively shunted piezoceramic. Similarly, an inductor across the piezoceramic is termed as a resonantly shunted piezoceramic. In this study, the effect of resistive shunting on the nature of damping enhancement to the host structure has been investigated. Analytical studies are presented along with experimental results.

Closed form solutions for element equilibrium and flexibility matrices of eight node rectangular plate bending element using integrated force method

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.

Filling Characteristics for an Activated Carbon Based Adsorbed Natural Gas Storage System

The storage capacity of an activated carbon bed is studied using a 2D transport model with constant inlet flow conditions. The predicted filling times and variation in bed pressure and temperature are in good agreement with experimental observations obtained using a 1.82 L prototype ANG storage cylinder. Storage efficiencies based on the maximum achievable V/V (volume of gas/volume of container) and filling times are used to quantify the performance of the charging process. For the high permeability beds used in the experiments, storage efficiencies are controlled by the rate of heat removal. Filling times, defined as the time at which the bed pressure reaches 3.5 MPa, range from 120 to 3.4 min for inlet flow rates of 1.0 L min(-1) and 30.0 L min(-1), respectively. The corresponding storage efficiencies, eta(s), vary from 90% to 76%, respectively. Simulations with L/D ratios ranging from 0.35 to 7.8 indicate that the storage efficiencies can be improved with an increase in the LID ratios and/or with water cooled convection. Thus for an inlet flow rate of 30.0 L min(-1), an eta(s) value of 90% can be obtained with water cooling for an L/D ratio of 7.8 and a filling time of a few minutes. In the absence of water cooling the eta(s) value reduces to 83% at the same L/D ratio. Our study suggests that with an appropriate choice of cylinder dimensions, solutions based on convective cooling during adsorptive storage are possible with some compromise in the storage capacity.

Study of symmetrical and related components through the theory of linear vector spaces

The paper proposes a study of symmetrical and related components, based on the theory of linear vector spaces. Using the concept of equivalence, the transformation matrixes of Clarke, Kimbark, Concordia, Boyajian and Koga are shown to be column equivalent to Fortescue's symmetrical-component transformation matrix. With a constraint on power, criteria are presented for the choice of bases for voltage and current vector spaces. In particular, it is shown that, for power invariance, either the same orthonormal (self-reciprocal) basis must be chosen for both voltage and current vector spaces, or the basis of one must be chosen to be reciprocal to that of the other. The original �¿, ��, 0 components of Clarke are modified to achieve power invariance. For machine analysis, it is shown that invariant transformations lead to reciprocal mutual inductances between the equivalent circuits. The relative merits of the various components are discussed.

Males, but not females, mate with multiple partners: a laboratory study of a primitively eusocial wasp Ropalidia marginata

The intense interest in social Hymenoptera, on account of their elaborate sociality and the paradox of altruism, has often suffered from considerable gender imbalance. This is partly due to the fact that worker behaviour and altruism are restricted to the females and partly because males often live off the nest. Yet, understanding the males, especially in the context of mating biology is essential even for understanding the evolution of sociality. Mating patterns have a direct bearing on the levels of intra-colony genetic relatedness, which in turn, along with the associated costs and benefits of worker behaviour, are central to our understanding of the evolution of sociality. Although mating takes place away from the nest in natural colonies of the primitively eusocial wasp Ropalidia marginata, mating can be observed in the laboratory if a male and a female are placed in a transparent, aerated plastic container, and both wasps are in the range of 5-20 days of age. Here, we use this setup and show that males, but not females, mate serially with multiple partners. The multiple mating behaviour of the males is not surprising because in nature males have to mate with a number of females, only a few of whom will go on to lay eggs. The reluctance of R. marginata females to mate with multiple partners is consistent with the expectation of monogamy in primitively eusocial species with totipotent females, although the apparent discrepancy with a previous work with allozyme markers in natural colonies suggesting that females may sometimes mate with two or three different males remains to be resolved.

New nine-node Lagrangian quadrilateral plate element based on Mindlin-Reissner theory using IFM

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations theta(x) and theta(y) are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.