A three-dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates. Suitable displacement functions that identically satisfy ...boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations, which are then solved by employing the power series method. The exact solution is valid for thick and thin plates, and for arbitrary variation of material properties in the thickness direction. Results are presented for two-constituent metal–ceramic functionally graded rectangular plates that have a power-law through-the-thickness variation of the volume fractions of the constituents. The effective material properties at a point are estimated by either the Mori–Tanaka or the self-consistent schemes. Exact natural frequencies, displacements and stresses are used to assess the accuracy of the classical plate theory, the first order shear deformation theory and a third order shear deformation theory for functionally graded plates. Parametric studies are performed for varying ceramic volume fractions, volume fraction profiles and length-to-thickness ratios. Results are also computed for a functionally graded plate that has a varying microstructure in the thickness direction using a combination of the Mori–Tanaka and the self-consistent methods. Forced vibrations of a plate with a sinusoidal spatial variation of the pressure applied on its top surface are scrutinized.
Abstract
We numerically find values of four process input parameters, namely, the argon flow rate, the hydrogen flow rate, the powder feed rate, and the current, that yield the desired mean ...particles’ temperature and the mean particle velocity (collectively called mean particles’ characteristics, or MPCs) in an atmospheric plasma spray process just before the particles arrive at the substrate to be coated. Previous studies have shown that the coating quality depends upon the MPCs. The process is simulated by using the software, LAVA-P-3D, that provides MPCs close to their experimental values. Thus, numerical rather than physical experiments are conducted. We first use the design of experiments to characterize the sensitivity of the MPCs to process parameters. We then identify relationships between the significant input parameters and the MPCs by using two methods, namely, the least squares regression and the response surface methodology (RSM). Finally, we employ an optimization algorithm in conjunction with the weighted sum method to find optimum values of the process input variables to achieve desired values of the MPCs. The effects of weights assigned to the objective functions for the temperature and the velocity, and the difference in using the regression and the RSM model have been studied. It is found that these values of the process parameters provide MPCs within 5% of their desired values. This methodology is applicable to other coating processes and fabrication technologies such as hot forging, machining and casting.
Vibrations of a fixed–fixed narrow microbeam electrostatically actuated by applying a voltage difference to it and a parallel rigid conductor are analyzed. For gaps between the two conductors that ...are comparable to the beam's thickness, the fundamental frequency of the beam may first increase with increasing applied voltage, before suddenly dropping at the pull-in voltage. Available models fail to accurately describe this behavior of the frequency versus voltage diagram for narrow microbeams, that results from a combination of strain-hardening and electrostatic softening effects. A distributed electromechanical model, that accounts for electrostatic fringing fields, finite deflections and residual stresses, is proposed. A recent estimate of the electrostatic force incorporating fringing fields due to both finite width and finite thickness of the microbeam is employed. The lowest frequency is extracted with a simple and computationally efficient one degree-of-freedom model obtained by approximating the deflection field with the static deflection of a fixed–fixed microbeam loaded by a uniformly distributed force. The model's predictions are in good agreement with those from three-dimensional finite-element simulations.
► Consideration of elasto-plastic deformations of the polymer matrix. ► Delineation of damage initiation and progression. ► Determination of initiation times of different failure modes. ► Comparison ...of time histories of computed and experimental contact loads.
We analyze the damage initiation, damage progression, and failure during 3-dimensional (3-D) elasto-plastic deformations of a fiber reinforced polymeric laminated composite impacted by a low speed rigid sphere, and compare computed results with experimental findings available in the literature. Damage is assumed to initiate when one of Hashin’s failure criteria is satisfied, and its evolution is modeled by an empirical relation proposed by Matzenmiller, Lubliner and Taylor. The transient nonlinear problem is solved by the finite element method (FEM). Contributions of the work include considering damage in 3-D rather than plane stress deformations of a laminated structure and elasto-plastic deformations of the composite. This has been accomplished by developing a user defined subroutine and implementing it in the FE software ABAQUS. From strains supplied by ABAQUS the material subroutine uses a micro-mechanics approach based on the method of cells and values of material parameters of constituents to calculate average stresses in an FE, and checks for Hashin’s failure criteria. If damage has initiated in the material, the subroutine evaluates the damage developed, computes resulting stresses, and provides them to ABAQUS. The damage evolved at a material point is not allowed to decrease during unloading. The delamination failure mode is simulated by using the cohesive zone model available in ABAQUS. The computed time histories of the axial load acting on the impactor are found to agree well with the experimental ones available in the literature, and various damage and failure modes agree qualitatively with those observed in tests.
A consistent one-dimensional distributed electromechanical model of an electrically actuated narrow microbeam with width/height between 0.5-2.0 is derived, and the needed pull-in parameters are ...extracted with different methods. The model accounts for the position-dependent electrostatic loading, the fringing field effects due to both the finite width and the finite thickness of a microbeam, the mid-plane stretching, the mechanical distributed stiffness, and the residual axial load. Both clamped-clamped and clamped-free (cantilever) microbeams are considered. The method of moments is used to estimate the electrostatic load. The resulting nonlinear fourth-order differential equation under appropriate boundary conditions is solved by two methods. Initially, a one-degree-of-freedom model is proposed to find an approximate solution of the problem. Subsequently, the meshless local Petrov-Galerkin (MLPG) and the finite-element (FE) methods are used, and results from the three methods are compared. For the MLPG method, the kinematic boundary conditions are enforced by introducing a set of Lagrange multipliers, and the trial and the test functions are constructed using the generalized moving least-squares approximation. The nonlinear system of algebraic equations arising from the MLPG and the FE methods are solved by using the displacement iteration pull-in extraction (DIPIE) algorithm. Three-dimensional FE simulations of narrow cantilever and clamped-clamped microbeams are also performed with the commercial code ANSYS. Furthermore, computed results are compared with those arising from other distributed models available in the literature, and it is shown that improper fringing fields give inaccurate estimations of the pull-in voltages and of the pull-in deflections. 1641
We use the first-order shear deformation theory (FSDT) coupled with the finite element method (FEM) to study free vibrations of a functionally graded (FG) anisotropic rectangular plate with the ...objective of maximizing one of its first five natural frequencies. The following edge conditions are considered: (i) all edges clamped, (ii) all edges simply supported, (iii) two opposite edges clamped and the other two free, and (iv) two opposite edges simply supported and the other two free. An advantage of a functionally graded plate over a laminated plate is that material properties vary continuously through the plate thickness. Thus no sudden discontinuities in stresses occur across an interface between any two adjoining laminae thereby eliminating the delamination mode of failure. Whereas there have been numerous works on studying the response of FG plates made of isotropic elastic constituents with the homogenized material also modeled as isotropic elastic (e.g., see Refs. 1, 2 and references cited therein), the only other study on FG anisotropic plate 3 has assumed that all elastic constants vary exponentially through the plate thickness at the same rate. It is highly unlikely that elastic moduli of a FG anisotropic plate will exhibit this property. Here we consider a FG anisotropic plate in which the fiber orientation varies smoothly through the plate thickness.
The local water slamming refers to the impact of a part of a ship hull on stationary water for a short duration during which high local pressures occur on the hull. We simulate slamming impact of ...rigid and deformable hull bottom panels by using the coupled Lagrangian and Eulerian formulation included in the commercial software LS-DYNA. We use the Lagrangian formulation to describe plane-strain deformations of the hull panel and consider geometric nonlinearities. The Eulerian formulation is used to analyze deformations of the water. Deformations of the hull panel and of the water are coupled through the hydrodynamic pressure exerted by water on the hull, and the velocity of particles on the hull wetted surface affecting deformations of the water. The continuity of surface tractions and the inter-penetrability of water into the hull are satisfied by using a penalty method. The computer code is verified by showing that the computed pressure distributions for water slamming on rigid panels agree well with those reported in the literature. The pressure distributions computed for deformable panels are found to differ from those obtained by using a plate theory and Wagner's slamming impact theory. We have also delineated jet flows near the edges of the wetted hull, and studied delamination induced in a sandwich composite panel due to the hydroelastic pressure.
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