Noded Isoparametric Element Research Articles

Analysis of Pile Group in Square Arrangement Embedded in Clayey Soil

Objective: The purpose of this study is to simulate and compare the response of the 3 × 3 pile group, embedded in clay, subjected to static lateral load, in terms of lateral deflection when soil is represented by different elastoplastic yield criteria. The effect of geometrical and material parameters is also investigated. Methods: In the developed finite element formulation, 20 node isoparametric elements have been used to model piles and pile caps. Surrounding soil has been modeled using 8-node isoparametric elements. The code is being developed in FORTRAN 90. Findings: The parametric study revealed the impact of the constitutive model to represent soil, pile spacing, pile length, pile diameter, and soil properties on the lateral deflection of the pile group. Mohr-Coulomb criterion predicts the lowest lateral displacement and maximum bending moment. An increase in spacing-to-diameter ratio from 2 to 6 causes a decrease in pile displacement by 80.13% in Von Misses, 70.3% in Drucker-Prager outer, 76.68% in Drucker-Prager inner, and 56.62% in Mohr-Coulomb yield criteria. An increase in the elastic modulus of soil from 20000 kPa to 60000 kPa results in a reduction in lateral displacement by 43.12% and an increase in pile diameter from .6 m to 1.0 m causes a reduction in lateral displacement by 82.73% when Von Mises criterion is used. The change in length-to-diameter ratio from 10 to 25 reduces pile displacement by 23.91%. Novelty: Among the Von – Mises, Mohr-Coulomb, Drucker–Prager (outer), and Drucker–Prager (inner) criteria, the Mohr-Coulomb criterion predicts the lowest lateral response for the 3 × 3 pile group. However, as the s/D ratio increases from 2 to 6, the difference in response is minimized. A marginal difference is found at the L/D ratio of more than 15. Applications: The developed three-dimensional finite element software can be used by pile designers to predict the response of laterally loaded pile groups. Keywords: Lateral load, Pile group, Pile spacing, Von Misses criterion, Mohr-Coulomb criterion, Drucker-Prager criterion, Lateral pile deflection

Effect of grading pattern on free vibration analysis of FGM plates carrying concentrated and distributed mass

The present article aims to develop a finite element formulation for FGM plates carrying concentrated and distributed mass. First-order shear deformation theory with consideration of physical neutral surface has been employed. Nine noded isoparametric element with five degrees of freedom at each node is used for this finite element analysis. To understand the effect of grading pattern under overhead mass carrying conditions, three types of FGMs have been analyzed. The effect of non-dimensional parameters such as aspect ratio, thickness ratio, power index, the intensity of mass etc. are extensively studied. It will bring new insights to the field of FGM structures.

Energy harvesting using variable stiffness piezolaminated shallow shell panels exposed to hygrothermal environments

The effect of hygrothermal environment on the energy harvesting capabilities of piezolaminated shallow shell panels made of variable stiffness composite layers (VSCL) is investigated. The use of curvilinear fibers to tailor the characteristics of the energy harvester is also explored. To model the deformation of the harvester, a finite element model based on a first-order normal shear deformation theory (FNSDT) is developed. Nonlinear strain–displacement relations based on Green–Lagrange strains are considered for nonuniform stress distribution due to temperature and moisture. A nine noded isoparametric element is used to discretize the domain. The effects of temperature and moisture concentration change on Power frequency response functions (FRFs), Voltage FRFs and Motion FRFs are presented. Power FRFs, Voltage FRFs and Motion FRFs are plotted for optimum load resistance when the shell structure is excited at short and open circuit frequencies. The current study is expected to help design and optimize the vibrational energy harvester to power sensors used in different automotive, aerospace, nuclear applications, subjected to elevated temperature and moisture conditions.

Thermoelastic free vibration of rotating tapered porous functionally graded conical shell based on non-polynomial higher-order shear deformation theory

This study uses a non-polynomial higher-order shear deformation theory to calculate the fundamental frequency of a rotating cantilevered porous functionally graded (FG) conical shell with variable thickness. Eight noded isoparametric shell elements having seven degrees of freedom per node are used to discretize the shell. Utilizing a simple power law, the temperature-dependent material characteristics of the FG conical shell are determined. The one-dimensional Fourier heat conduction equation is used to obtain the nonlinear temperature distribution. Lagrange’s equation is used to derive the dynamic equation of motion. Finally, a parametric study is presented.

Nonlinear Behavior of Fgm Skew Plates Under In-Plane Load

Nonlinear behavior of Functionally Graded Material (FGM) skew plates under in-plane load is investigated here using a shear deformable eight noded iso-parametric plate bending finite element. The material is graded in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. The effective material properties are estimated using Mori-Tanaka homogenization method. The nonlinear governing equations for the FGM plate under in-plane load are solved by Newton-Raphson technique to obtain the out-of-plane central deflection and in-plane displacement of the loaded edge. The existence of bifurcation-type of buckling for FGM plates is examined for different boundary conditions, constituent gradient index, and skew angle.

Dynamic Analysis of Laminated Composite One-fold Plates under Thermal Load

In this research, free vibration analysis of epoxy-based laminated composite folded plate structures for thermal loads have been considered using finite element method. Eight noded isoparametric element with five degrees of freedom per node have been considered in the study. Folded plate formulation using 6 X 6 transformation matrix is applied to transform the element mass and stiffness matrices to global system matrices. Yang-Norris-Stavsky (YNS) theory along with rotary inertia have been used in the present formulation. Lamina material properties at elevated temperature have been used in the study. Parametric studies have been performed for laminated composite one-fold plate structure for various thicknesses, crank angle and fibre angle under different temperatures. Results reveal that rising thermal load reduces the stiffness of the structure considerably. As the presence of fold increases stiffness of the plate structures significantly, it can withstand increased temperature. Proper choice of fibre angle and thickness increases the stiffness of the structures thus making it more capable of resisting higher thermal load.

Dynamic Analysis of Simply Supported Functionally Graded Plates

Functionally graded materials (FGMs) are considered as a special composite material that is synthesized for a specific purpose by gradual mixing of two or more different materials thus with varying material properties through their thickness. Due to smooth and continuous varying material properties from one face to another, FGMs are usually superior to the conventional composite materials in mechanical behavior. Hence the dynamic analysis of FGM plates is essential. In this paper, numerical solutions for free vibration analysis of moderately thick plates composed of functionally graded materials with simply supported boundary conditions using finite element analysis have been studied. First-order shear deformation plate theory (FSDT) has been applied in the research. Eight noded isoparametric serendipity plate bending elements have been used. Young’s modulus and density per unit volume are assumed to vary continuously through the plate thickness according to a power-law distribution. The results have been validated with the existing literature available from other analytical and numerical techniques. The effect of different plate parameters such as aspect ratios, edge constraints, thickness to length ratios, and gradient indices on the natural frequencies of FG rectangular plates are presented. It is found that the natural frequency depends considerably on the said parameters.

Aeroelastic control of delaminated variable angle tow laminated composite plate using piezoelectric patches

The free vibration and aeroelastic analysis of variable angle tow (VAT) laminated composite plate bonded with discrete piezoelectric patches are considered for investigation. A finite element (FE) model is developed using eight noded isoparametric elements to study the impact of delamination size and location on the dynamic response of smart VAT laminated plates. For aeroelastic analysis, the FE model is coupled with MSC. Nastran through Direct Matrix Abstraction Program (DMAP) and the structural parameters obtained with the FE model are supplied to MSC. Nastran solver to generate aerodynamic force matrix using Doublet Lattice Method (DLM). Various parametric studies are performed to find the most critical location of the delamination that severely affects vibration and flutter characteristics. The results showed that the delamination near the leading edge which faces free stream wind is found to be the most critical for the dynamic aeroelastic failure of structures. Further, the most effective location of the piezoelectric patches is identified to enhance the aeroelastic boundary of smart delaminated VAT composite plates using active displacement and velocity feedback gains.

A Node-Based Strain Smoothing Technique for Free Vibration Analysis of Textile-Like Sheet Materials

This paper presents an implementation of the node-based smoothed finite element method and Reissner-Mindlin plate theory for a four node isoparametric shell element to improve the numerical precision and computational efficiency subjected to free vibration analysis of textile-like sheet materials. A one smoothing cell integration scheme in the strain smoothing technique is implemented to contrast the shear locking phenomenon that may exists in the analysis for moderately-thick and thick shell models. Various numerical results of free vibration analysis for a multi-layer nonwoven fabric sample are compared with other existing analytical solutions and numerical solutions in literatures to demonstrate the effectiveness of the present method. An advantage of the present formulation is that it can improve the numerical precision without decreasing the computational efficiency.

An Alpha Finite Element Method for Linear Static and Buckling Analysis of Textile-Like Sheet Materials

A four node isoparametric shell element (Q4) based on Mindlin/Reissner plate theory and the alpha finite element method (αFEM) was formulated for a nearly exact solution of linear static and buckling analysis of textile-like sheet material. The novel idea of αFEM-Q4 is assumed to be similar to the framework of conventional finite element approaches for Q4, but the gradient of strains is scaled by a factor α ∈ [0, 1]. The numerical examples demonstrate that the αFEM-Q4 can improve the accuracy of FEM solution in static and buckling analysis shell structures of non-woven fabric. However, the αFEM-Q4 cannot provide the nearly exact solution to all elasticity problems. In addition, it also requires a quadrilateral mesh that cannot be fully generated by common geometric algorithms for complicated problem domains.

A solution for free vibration of rotating hybrid multiscale nanocomposite conical shell

In the present investigation, first-order shear deformation theory (FSDT) is employed to conduct free vibration analysis of hybrid CNT-fiber nanocomposite conical shells using finite element approach. The effective material properties of this three phase nanocomposite is computed using Halpin- Tsai and Micro-mechanics model approach. The Lagrange’s equation of motion is used to derive the equilibrium equations of the rotating carbon nanotube – fibre nanocomposite conical shell wherein the nonlinearity due to rotation is also introduced. The Coriolis effect is neglected because of the moderate rotational speed of the shell. Finite element code is developed using eight noded isoparametric shell element and the same is validated with some literature to analyse the effect of twist angle, length to thickness ratio, aspect ratio, weight fraction of CNTs, and rotational speed on the fundamental frequency. The effect of such parameter on the mode shapes of the three phase nanocomposite shell are also presented here.

Axial and Shear Buckling Analysis of Multiscale FGM Carbon Nanotube Plates Using the MTSDT Model: A Numerical Approach.

The present paper investigates the axial and shear buckling analysis of a carbon nanotube (CNT)-reinforced multiscale functionally graded material (FGM) plate. Modified third-order deformation theory (MTSDT) with transverse displacement variation is used. CNT materials are assumed to be uniformly distributed, and ceramic fibers are graded according to a power-law distribution of the volume fraction of the constituents. The effective material properties are obtained using the Halpin–Tsai equation and Voigt rule of the mixture approach. A MATLAB code is developed using nine noded iso-parametric elements containing 13 nodal unknowns at each node. The shear correction factor is eliminated in the present model, and top and bottom transverse shear stresses are imposed null to derive higher-order unknowns. Comparisons of the present results with those available in the literature confirm the accuracy of the existing model. The effects of material components, plate sizes, loading types, and boundary conditions on the critical buckling load are investigated. For the first time, the critical buckling loads of CNT-reinforced multiscale FGM rectangular plates with diverse boundary conditions are given, and they can be used as future references.

STRESS DISTRIBUTION IN THE HOLLOW STIFFENED HYBRID LAMINATED COMPOSITE PANELS IN SHIP STRUCTURES UNDER SINUSOIDAL LOADING

A simplified hollow stiffened hybrid laminated plate model has been developed for the marine structures. The detailed stress analysis through the thickness of the stiffened plate based on the higher order shear deformation theory has been carried out under sinusoidal loading. The hybrid laminates are made by wrapping the GFRP laminates with CFRP at the outermost layers of the stiffened panel. This hybridization technique can be an optimum solution from the point of view of cost reduction as well as enhancement of strength properties. The layer-wise stresses for the stiffened plate have been calculated in the present paper. A 3D polynomial curve fitting technique has been used to obtain higher accuracy and consistency in the computation of stresses. The computer code has been developed using MATLAB considering the plates as eight noded isoparametric plate bending element and the stiffener has been modeled as three noded isoparametric beam element. The stiffened panel has also been analysed using the ANSYS14.0 software package considering 2D model. The results obtained from the present formulation have been compared with those available in the published literature to validate the present formulation. The stiffened panels made of GFRP, CFRP and GFRP-CFRP hybrid laminates have been studied here. An extensive parametric study has been carried out with varying fibre content in the laminates.

FREE VIBRATION OF SKEW LAMINATES – A BRIEF REVIEW AND SOME BENCHMARK RESULTS

This study investigates and reviews prior research works on skew composite laminates. The equivalent single layer theories are explored and discussed. An exhaustive review on static and dynamic analysis of composite skew laminates is also presented. Subsequently, a nine node isoparametric plate bending element is used for free vibration analysis of laminated composite skew plate with central skew cut out. The effect of shear deformation is incorporated in the formulation considering first order shear deformation theory. Two types of mass lumping schemes are analysed to study the effect of rotary inertia. Certain numerical examples of plates having different skew angles, skew cut out sizes, boundary conditions, thickness ratios (h/a), aspect ratios (a/b), fiber orientations and number of layers are solved which will be useful for benchmarking of future studies.

A solution to free vibration of rotating pretwisted hybrid CNTs multiscale functionally graded conical shell

In the present study, the free vibration analysis of multiscale functionally graded (FG) carbon nanotube (CNT)–metal–ceramic composite conical shells is conducted using finite element methodology. Using first-order shear deformation theory (FSDT) strains are computed and an eight noded isoparametric shell element is used in the present formulation. Dynamic equation is derived using Lagrange’s equation of motion for moderate rotational speeds wherein Coriolis effect is neglected. The finite element code is developed and validated with the existing literature to analyze the effects of power law index, weight fraction of CNTs, length to thickness ratio, aspect ratio, twist angle and rotational speeds on fundamental natural frequency. Mode shapes of both twisted and untwisted conical shells under varying rotating conditions are also presented.

Finite element analysis of smart composite plate structures coupled with piezoelectric materials: Investigation of static and vibration responses

This research presents a generalized-energy-based finite element modeling of smart composite plates with distributed piezoelectric materials for the static and vibration responses under electrical and mechanical loading. The zigzag kinematics in conjunction with a non-polynomial higher-order shear deformation theory is used to derive the model. The plate theory accounts for the non-linear variations of the transverse shear strains across the thickness of the plates and also accommodates the inter-laminar continuity effects of transverse shear stresses at the interfaces. Eight noded isoparametric serendipity elements are used to discretize the physical domain. The solutions in the time domain are obtained from the discretized system of ordinary differential equations with Newmark’s time integration scheme. Several numerical examples are solved for different types of smart composite plates with various piezoelectric materials, boundary conditions, static and dynamic loadings. The classical negative feedback controller is used for deriving the suppressed and controlled vibration responses of the smart composite plates with distributed actuators and sensors. A comparison of the present FE solutions with the elasticity and other analytical and numerical solutions shows good agreement, thereby ensures the applicability of the present finite element model for studying the coupled electromechanical problems of piezoelectricity.

Uncertainty quantification in buckling strength of variable stiffness laminated composite plate under thermal loading

In this paper, thermal buckling analysis of variable stiffness composite laminate (VSCL) is carried out. The first-order shear deformation theory is adopted with eight noded isoparametric element to construct a finite element model for thermal buckling analysis. The effect of the uncertain composite properties that could arise due to complex manufacturing and fabrication process to the buckling temperature is investigated using polynomial neural network (PNN). The contribution of individual properties, such as the material properties, fiber orientations, and the thermal expansion coefficients of VSCL plate are performed for various boundary conditions and lamination sequences. A sensitivity analysis is also carried out and parameters to which buckling temperature has high sensitivity are identified. The accuracy and efficiency of PNN model are compared with Monte Carlo simulation (MCS). Further, PNN is employed to evaluate the reliability parameters of VSCL plate. From the various studies, it is observed that even though the influence of different stochastic input parameters are depend on the boundary conditions, the transverse coefficient of thermal expansion (α22) is found to be most influential parameter, followed by transverse (E22) and longitudinal (E11) Young’s modulus, respectively.

Influence of Scoured Beds on The Characteristics of Seepage underneath Structures.(Dept.C)

In this paper, the effect of the scoured beds on the characteristics of seepage underneath heading up structures, has been studied numerically using Finite Element technique. Five assumptions of the eroded beds have been considered to achieve the behaviour of flow under the structure. The three and four node isoparametric elements have been illustrated the uplift pressure acting on the floor of the structure while the rate of seepage flow increases. The floor creep velocities and exit gradients for the studied cases have been illustrated.

Finite element prediction of first-ply failure loads of composite thin skewed hypar shells using nonlinear strains

The application of skewed hypar shell as civil engineering roofing unit is an established fact. Such use has gained a greater momentum when this shell is fabricated with advanced materials like the laminated composites. Research attempts in studying the first ply failure behaviour of laminated composite structural units are common now among engineers and the novelty of this paper lies in continuation of such efforts being applied to composite skew hypar shell. For accurate modelling of the failure behaviour of this thin shell, nonlinear strains are considered together with eight noded isoparametric serendipity finite element. Different well-established failure criteria including the failure criterion of Puck are used to extract the first ply failure pressure values, failure locations and failure modes as well. The finite element code developed is used for numerical experimentation with parametric variations and the results are post processed and interpreted to extract meaningful engineering conclusions.

A modified higher order zigzag theory for response analysis of doubly curved cross-ply laminated composite shells

The present theory deals with static and free vibration analyses based on higher order zigzag theory for laminated composite shells. The finite element shell model is developed considering the thickness coordinate to radius ratio (z/R) using nine noded isoparametric quadratic element. The proposed formulation satisfies the interlaminar stress continuity at the interface of laminae and zero shear boundary conditions at free surfaces. The response results obtained by the proposed formulations are compared with the published results. Moreover, new responses results of hyperbolic paraboloidal laminated shells are obtained using the present laminated shell theory and illustrated in the present study.