Determining Green's function for a plate of variable thickness, rectangular in the plan
Reciprocal theorem used to determine Green function for plate of variable thickness, rectangular in plan
RECTANGULAR PLATE↗
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Calculation of rectangular orthotropic plates lying on an elastic foundation with two foundation moduli and subjected to static and pulsating loads
Method of initial parameters used in differential equations for bending and internal stress forces occurring in rectangular orthotropic plates lying on elastic foundation
RECTANGULAR PLATE↗
Bending of an elastic thin plate supported by rigid columns
Systems of equations defining bending occurring in finite isotropic elastic thin plate supported by rigid or yielding columns
ELASTIC PLATE↗
On dynamic response of a rectangular plate to a series of moving loads
Dynamic response of rectangular plate to series of moving loads
ELASTIC PLATE↗
The maximum response of rectangular plates to random excitation
Maximum response of rectangular plates to random excitation
EXCITATION↗
A unified theory of plastic buckling of columns and plates
On the basis of modern plasticity considerations, a unified theory of plastic buckling applicable to both columns and plates has been developed. For uniform compression, the theory shows that long columns which bend without appreciable twisting require the tangent modulus and that long flanges which twist without appreciable bending require the secant modulus. Structures that both bend and twist when they buckle require a modulus which is a combination of the secant modulus and the tangent modulus. (author)
PLATES - PLASTICITY↗
Linear Integro-differential Schroedinger and Plate Problems Without Initial Conditions
Via Carleman's estimates we prove uniqueness and continuous dependence results for the temporal traces of solutions to overdetermined linear ill-posed problems related to Schroedinger and plate equation. The overdetermination is prescribed in an open subset of the (space-time) lateral boundary.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On a Class of Nonlinear Viscoelastic Kirchhoff Plates: Well-Posedness and General Decay Rates
This paper is concerned with well-posedness and energy decay rates to a class of nonlinear viscoelastic Kirchhoff plates. The problem corresponds to a class of fourth order viscoelastic equations of p-Laplacian type which is not locally Lipschitz. The only damping effect is given by the memory component. We show that no additional damping is needed to obtain uniqueness in the presence of rotational forces. Then, we show that the general rates of energy decay are similar to ones given by the memory kernel, but generally not with the same speed, mainly when we consider the nonlinear problem with large initial data.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form
We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of the method with respect to the plate thickness.
97 MATHEMATICS AND COMPUTING↗
Biaxial Bending of an Isotropic Plate with Through Rectilinear Crack with Regard for the Width of the Contact Zone of its Edges and in the Presence of Plastic Zones Near its Tips
We pose and solve the problem of the biaxial bending of an isotropic plate with through rectilinear crack by distributed bending moments applied at infinity. The edges of the crack are in contact over the zone of constant width and plastic zones are formed near the crack tips. By using the Tresca plasticity conditions in the form of a surface layer and a plastic hinge, we determine the length of the plastic zone and the crack opening displacements near the tips. The numerical analysis of the problem is performed.
42 ENGINEERING↗
Viscoelastic Stresses in the Plates Containing Inclusions with Cracks
We study viscoelastic stresses in the plates containing inclusions weakened by cracks by the method of boundary integral equations and the Laplace integral transformation. The case in which the rheological relations between stresses and strains are written in the differential form is analyzed in detail. To solve the boundary problem of viscoelasticity, we use the well-known approach in which the corresponding problem of the theory of elasticity is studied by replacing the differential operators with constant quantities. The solution of the auxiliary problem is obtained by the method of boundary integral equations reduced to a system of algebraic equations. After replacing the elastic quantities in this system by the corresponding differential operators, we solve the system obtained as a result by using the Laplace integral transformation and then applying the improved numerical-analytic inversion formula adapted to this class of problems.
36 MATERIALS SCIENCE↗
Microstructure and Performance of Nano-WC Particle-Strengthened Ni Coatings by Electro-brush Plating
Nano-WC particle-strengthened Ni composite coatings were prepared by electro-brush plating. A series of artificial neural network models was developed for the analysis and prediction of the coating performance. The microstructure and phase structure were studied with SEM, XRD and EDS. Nano-WC particles as the hard phase were distributed evenly and dispersed in the coatings, which was conducive to the hardness enhancement of the coatings. Additionally, nano-WC particles as microballs inserted in the coatings could reduce the friction when wear of the coating surface occurred. Furthermore, the addition of nano-WC particles delayed the time of crack initiation and propagation in the coatings, which increased the service lifetime when they worked in a thermal shock environment.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Preparation and Oxidation Performance of a NiCoCrAlYSiHf + NiAl Composite Coating Deposited by Arc Ion Plating and Magnetron Sputtering Techniques
A NiCoCrAlYSiHf+NiAl composite coating was deposited onto a second-generation single-crystal superalloy René N5 by methods of arc ion plating and magnetron sputtering. After vacuum annealing, the composite coating exhibited a gradient distribution of elements, in which Al was enriched in outer layer and Cr was enriched in inner layer. Compared with conventional NiCoCrAlYSiHf and β-NiAl coatings, the composite coating was evaluated in isothermal and cyclic oxidation tests at 1100 °C in ambient air. The results showed that the oxidation rate of the composite coating was lower than that of NiCoCrAlYSiHf coating. Meanwhile, the extent of interdiffusion between coating and substrate in the composite coating was slighter compared with that in the β-NiAl coating. Microstructure evolutions of the composite coating after annealing and further oxidation test are investigated.
36 MATERIALS SCIENCE↗
Numerical Simulation of Residual Stresses in Multipass Gas Metal Arc-Welded Joints of Thick Aluminum Alloy Plates
Numerical simulation was utilized to investigate the residual stresses in the multipass gas metal arc-welded joints of high-strength Al-Zn-Mg alloy plates. In order to elevate the reliability of numerical simulation, the heat source model, parameters characterizing the thermal and mechanical properties, boundary conditions, material constitutive model and finite element meshing were discussed in detail. As a novelty of this paper, the modified Arrhenius constitutive equation of the base material and the filled material was obtained according to the results of high-temperature tensile tests. Distributions of stress on the upper and bottom surface of the joint were obtained based on numerical simulation. Special attention was paid to the evolutions of local residual stress on the bottom surface of the joint, and it’s found that residual stresses on the bottom surface of the joint were almost unchanged after the weld seam approached a certain thickness. Blind-hole method and x-ray method were adopted to detect the residual stresses on the surfaces to verify the accuracy of the results obtained by numerical simulation.
36 MATERIALS SCIENCE↗
Impact Damage Investigation on Glass Fiber-Reinforced Plate Laminates at Room and Lower Temperatures through Ultrasound Testing and Electronic Speckle Pattern Interferometry
In this work, the evaluation of damage area due to low-velocity impact tests at different impact energy values and different temperatures on glass fiber-reinforced plate laminates was investigated by two nondestructive evaluation (NDE) techniques, electronic speckle pattern interferometry (ESPI) and ultrasound testing (UT). Composites are characterized by several interacting failure modes such as matrix breakage, fiber failure and delaminations, which can be simultaneously induced by low-velocity impacts and can be different depending on the temperature. It can be complicated to detect by visual inspections of the structures for such phenomena. This paper aims to investigate the dependence of the damaged area with respect to temperature variation on glass fiber composite laminates. GF composite laminates were impacted with three energy levels (5, 10, 20 J) and at different temperatures (room temperature, − 25, − 50 °C) by a drop weight impact machine. The results show that at decreasing temperature, a decrease in the damage extension was observed, which is more evident at increasing impact energy. Moreover, as expected, the results confirm UT and ESPI techniques are able to identify the barely visible low-velocity impact damage. However, some limitations for detection were found in ESPI. Nonetheless, the ESPI technique can be considered as one of the useful NDE methods if the calibration and the post-processing methods are improved.
36 MATERIALS SCIENCE↗
Direct shear strength of rebar-coupler anchor systems for steel-plate composite (SC) walls
This work focuses on the direct shear behavior of rebar-coupler anchor systems, and their use for anchorage of steel-plate composite (SC) walls to the concrete basemat of safety-related nuclear facilities. Large-scale rebar-coupler anchor specimens were tested under direct shear loading until failure. The results included the applied load-slip displacement responses of the specimens, the direct shear strength, and the observed failure mode. The American Concrete Institute (ACI) 349 code equation for calculating the direct shear strength of embedded anchors was compared with the direct shear strengths from the tests. The code equation underestimated the direct shear strength of the anchor system, because it was based on the assumption that shear failure occurs in the rebars, whereas experimental observations indicated that shear fracture failure occurred in the coupler rather than the rebars. The design equation was updated to utilize the net shear area of the coupler instead of the rebars, after which the direct shear strengths from the tests could be calculated with reasonable accuracy. The experimental results were also used to propose an empirical model for the shear force-slip displacement response of rebar-coupler anchor systems.
42 ENGINEERING↗
Impact of Backing Plate and Thermal Boundary Conditions for High-Speed Friction Stir Welding of 25-mm Thick Aluminum Alloy 7175-T79
Here this study demonstrates high-speed (150 mm/min) single pass friction stir butt joining of 25 mm thick aluminum alloy 7175-T79. To understand the impact of quenching and cooling rate on process responses, joint strength, and grain size distributions across the weld thickness, we performed a series of friction stir welding (FSW) trials in air and with a trailing water spray using steel and composite backing plates (BP). Welds made in air and trailing water spray exhibit significantly different hardness distributions across the nugget, heat affected zone (HAZ), and HAZ minimum hardness as evidenced by detailed microhardness mapping. The effect of trailing water spray (TWS) on joint efficiency overshadows the influence of BP composition due to the vastly different contribution to quenching. TWS also resulted in a multifaceted effect on FSW such as lowering processing temperature, increasing X and Z forces while lowering Y force, and narrow heat affecting zone. Finally, digital image correlation (DIC)-based fracture mode analysis and grain size measurements correlate with the hardness distribution.
42 ENGINEERING↗
Experimental and Numerical Investigation on Vibration of Sandwich Plates with Honeycomb Cores Based on Radial Basis Function
The vibration characteristic of the sandwich plate with a honeycomb core was investigated by experimental measurements and numerical calculation based on radial basis function (RBF). RBF method was used not only in the meshless approach but also in the post-processing of the experimental data. During the experiment, amplitude-fluctuation electronic speckle pattern interferometry was applied to access the resonant frequencies and the corresponding vibration mode shapes simultaneously. Then RBF method was used to improve the quality of patterns and reconstruct the out-of-plane vibration amplitude after fringe analysis. As for numerical calculation, the modal parameters were numerically predicted using the first-order shear deformation theory. The computation approach was based on collocation with multi-quadric radial basis function. To understand the influence of the thickness of face sheet on dynamic behaviors, three types of specimens with different thickness were tested and analyzed. Of particular interest was that the vibration modes show veering due to the thickness increment. Furthermore, the numerical predicted results were compared with the experimental measurements for the first five modes. They are in good agreement with each other for resonant frequencies, mode shapes and relative out-of-plane amplitudes.
36 MATERIALS SCIENCE↗
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