The features of the numerical solution of the two-dimensional equation of stationary heat conduction are considered taking into account nonlocal effects. The finite element method using isoparametric ...finite elements was chosen as the numerical solution scheme. A method for approximating the zone of nonlocal influence was proposed, and an estimate of the time for calculating the coefficients of the thermal conductivity matrix was also constructed. The influence of the main parameters of the model on the final results is studied, and a polynomial family of functions of non-local influence is also studied. The results are compared with the results obtained with the classical approach.
This paper proposes new analytical and finite element solutions for studying the effects of elastic foundations on the uncontrolled and controlled static and vibration responses of smart ...multi-layered laminated composite plates with integrated piezoelectric layers, acting as actuators and sensors. A non-polynomial higher-order plate theory with zigzag kinematics involving a trigonometric function and a local segmented zigzag function is adopted for the first time for modeling the deformation of a smart piezoelectric laminated composite plate supported on an elastic foundation. This model has only five independent primary variables like that of the first-order shear deformation theory, yet it considers the realistic parabolic behavior of the transverse shear stresses across the thickness of the laminated composites plates, and also maintains the continuity conditions of transverse shear stresses at the interfaces of the laminated plates. A two-parameter foundation model, namely Pasternak’s foundation, is used to model the deformation and shear interactions of the elastic foundation. The governing set of equations is derived by implementing Hamilton’s principle and variational calculus. Two different solution methods, namely, a generalized closed-form analytical solution of Navier-type, and a C
0
isoparametric finite element (FE) formulation, are developed for solving the governing set of equations. The solutions in the time domain are obtained with Newmark’s average acceleration method. Comprehensive parametric studies are presented to investigate the influence of elastic foundation parameters, piezoelectric layers, loading, and boundary conditions on the static and dynamic responses of the smart composite plates with piezoelectric layers. The effects of the elastic foundations on the vibration control of the smart composite plates are also presented by coupling the piezoelectric actuator and sensor with a feedback controller. Several benchmark results are presented to show the influence of the various material and geometrical parameters on the controlled and uncontrolled responses of the smart plates, and also the significant effect of the elastic foundations on the static and dynamic responses of the smart structures. The results obtained are in very good agreement with the available literature, and it can be concluded that the proposed analytical solution and FE formulation can be efficiently used to model the static and dynamic electro-elastic behavior of smart laminated plates supported on elastic foundations.
•A particle tracking algorithm for parallel finite element applications is proposed.•The algorithm is designed to work with 2D and 3D applications on unstructured grids with curved edges and ...non-planar faces.•The algorithm proposed can be effectively coupled with fluid flow applications in a parallel framework.
Numerical simulations of a particle tracking algorithm on parallel unstructured finite element grids are presented. The algorithm is designed to work for both 2D and 3D applications. To determine the position of the particle relative to the mesh, a new point-locating algorithm is proposed. The advection of the particle is performed on the physical domain in order to treat completely unstructured grids. As a consequence, the inversion of the isoparametric finite element mapping is requested. We comply with this demand implicitly using Newton–Raphson’s iteration for linear, quadratic, bi-quadratic and tri-quadratic finite elements, and several element geometries, including quadrilaterals, triangles, tetrahedra, wedges and hexahedra. To investigate the performances of the proposed algorithm, results of standard numerical tests are shown, together with a fluid flow application that exemplifies an instance of a particle tracking problem.
The present article deals with flexural and vibration response of functionally graded plates with porosity. The basic formulation is based on the recently developed non-polynomial higher-order shear ...and normal deformation theory by the authors’. The present theory contains only four unknowns and also accommodate the thickness stretching effect. The effective material properties at each point are determined by two micromechanics models (Voigt and Mori–Tanaka scheme). The governing equations for FGM plates are derived using variational approach. Results have been obtained by employing a C
0
continuous isoparametric Lagrangian finite element with eight degrees of freedom per node. Convergence and comparative study with the reported results in the literature, confirm the accuracy and efficiency of the present model and finite element formulation. The influence of the porosity, various boundary conditions, geometrical configuration and micromechanics models on the flexural and vibration behavior of FGM plates is examined.
The present article investigates the effect of elliptical cutouts and geometric imperfections on the vibrational response of functionally graded material (FGM) sandwich plates. Generalised governing ...equations for the sandwich FGM (SFGM) plate are derived based on non-polynomial higher-order shear deformation theory. Geometric discontinuities have been incorporated as elliptical cutouts in the plates, and the various geometric imperfections are modelled using the generic function. The mathematical modelling has been carried out using the C
continuity isoparametric finite element formulation by considering four-noded elements with seven degrees of freedoms per node. Convergence and validation studies have been performed to demonstrate the efficiency and accuracy of the present methodology. The influence of volume fraction index, geometric imperfections, and elliptical cutouts on the vibrational frequency of SFGM plates have been analysed under the mixed boundary conditions.
Dynamic deformation and rupture of fastening elements Ryabov, Alexander A.; Kukanov, Sergey S.; Strelets, Dmitry Yu ...
Journal of the Brazilian Society of Mechanical Sciences and Engineering,
03/2022, Letnik:
44, Številka:
3
Journal Article
Approach to numerical modeling of elastic–plastic dynamic deformation and rupture of the steel screws on the basis of numerical-experimental strain-based failure criterion in conditions of multiaxial ...states of stress under pulsed tension is presented in the paper. The equation of motion based on the variation principle of balance of virtual powers of work and Prandtl–Reuss flow rule is used to describe elastic–plastic deformations of the screws. A friction is taken into account at contact interaction between the turns of thread. Numerical solution of the problem is based on space discretization by finite element method and explicit scheme of numerical integration in time for equation of motion of deformable solids. The mesh model is built with 8-node isoparametric finite elements with sizes of
Δ
h
~ 0.2–0.4 mm. Validity of computer simulation using Russian code LOGOS is supported by proximity of numerical and experimental data for loading impulses and displacements at specific points. Analysis of the different state of stress parameters during deformation process up to failure of screws is also presented. The developed computing modeling technology allows defining a local zone and level of maximal plastic equivalent strain at the third thread groove of the screw. Different parameters characterizing the type of state of stress at the point of maximum plastic deformations in the thread and on the screw axis are considered. Analysis shows that fractures occur in the cavity of the third thread of the screw under triaxial tension stress conditions at strain intensity significantly exceeding the relative elongation of the material. Fracture growth pattern is also presented in the paper.
The present paper deals with free vibration analysis of laminated composite skew plates with and without cut-outs. The experimental investigation along with numerical simulation has been presented in ...this paper for complete understanding of the dynamic behaviour of laminated skew plates with cut-out. Glass fibre-reinforced laminated composite plates have been prepared by resin infusion process using vacuum bagging technique in the laboratory for experimental analysis. The experimental studies have been carried out on skew composite plates with varying size of cut-out placed at the centre. The numerical analysis has been carried out by developing a computer code in MATLAB. Special attention is drawn on the formulation of mass matrix by considering effect of rotary inertia. The results obtained by the finite element formulation using nine-noded isoparametric plate-bending elements are validated by comparing the results from relevant published literature. The numerical and experimental data are then compared for experimental verification of present investigation. The consistency of mode shapes between experimental and numerical investigations is checked by using modal assurance criteria.
Abstract
The theory of the strength of load-bearing structural elements made of steel I-beams suggests that the nature of the stress distribution in the element is known, including from the action of ...concentrated pressure. A concentrated load is often applied at the level of the upper girdle of the beams, and causes local stresses in the wall. The walls of steel I-beams, due to their insignificant thickness, are sensitive to local pressure. That is why it is necessary to accurately determine the most stressed sections of the wall and the intensity of local stresses. In this paper, we consider a test model of a steel I-beam with a span of 9 m, to the upper girdle of which a concentrated load of 200 kN is applied. The local stresses in the wall are determined by analytical and numerical methods. The numerical calculation of the beam model was performed in the SCAD Office computing complex. The beam is modeled from volumetric isoparametric finite elements. The length of the beam wall is divided by two-sided stiffeners into nine compartments, with a step of 1000 mm. A comparative analysis of the nature of the distribution of local stresses in the wall of a steel beam obtained by analytical and numerical calculations is presented. Recommendations are given on taking into account local stresses in the beam wall from the action of a concentrated load when calculating strength.
A new dynamic model of a variable-length rope, which could be used for the transient analysis of a buoy-rope-generator (BRG) wave energy system, was proposed in this paper. The model started from the ...basic dynamic equations of variable mass system, and took into account the physical properties such as axial force, shear and bending. According to the principle of D’Alembert-Lagrange, the equivalent integral weak formulation was firstly obtained, and through consistent linearization and isoparametric discretization, the finite element model of the variable-length rope was then derived. The Bathe scheme was employed to solve the model numerically, based on its excellent performance in solving nonlinear dynamic problems, and an automatic time step size algorithm was designed according to the number of iterations of the two substeps of Bathe scheme. The procedures of rope mesh regeneration were also put forward, where only one variable-length element was always located at the top end of the rope, and the rest were all fixed-length elements. The proposed variable-length rope model and solution schemes were verified through comparison with the results of a tank experiment. Finally, the transient dynamics of a kind of BRG system was analyzed and discussed.
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