Plate Edge Conditions Research Articles

A hybrid boundary element method based model for wave interaction with submerged viscoelastic plates with an arbitrary bottom profile in frequency and time domain

This study investigates the scattering of surface ocean waves by a submerged viscoelastic plate placed over the variable bottom topography under the assumptions of linear theory. The solution is derived using the hybrid boundary element method. The boundary element method is faster and easier to use when compared to the most widely used analytical method, such as the eigenfunction expansion method. Moreover, the application of analytical methods is restricted to structures with regular geometries and flat sea bottom. However, the present solution technique works for the plate at any angle placed over the variable bottom topography. Furthermore, as a particular case, the scattering problem is analyzed when a rigid wall is placed downstream. Energy balance relations are derived to check the accuracy of the computed numerical results. The effect of sinusoidally varying bottom topography, damping parameter, and plate edge conditions on the Bragg resonance phenomenon is analyzed. Initially, the solutions are presented in the frequency domain using the hybrid boundary element method and then extended to the time domain using the Fourier transform. It is observed that when the edges of the submerged plate are fixed, the Bragg resonance occurs at lower values of the frequency parameter. However, the Bragg resonance occurs around the primary Bragg value when the plate has free edges. For certain incident wave frequencies, the viscoelastic plate that completely covers the undulating bed dissipates a greater amount of wave energy than when the plate only partially covers the seabed.

Mathematical modeling of a submerged piezoelectric wave energy converter device installed over an undulated seabed

A piezoelectric wave energy converter (PWEC) device integrated with an impermeable breakwater placed over an undulated seabed is considered. The PWEC device is composed of a single submerged flexible plate with piezoelectric layers attached to both faces of the flexible plate. Due to the piezoelectric effect, this piezoelectric plate generates electricity when excited by the incident waves. A detailed analysis is done to investigate the effect of PWEC plate submergence depth, plate length, plate edge conditions, incident wave period, bottom ripple amplitude, and ripple number on the power generation by the PWEC device. It is seen that the PWEC device edge conditions, submergence depth, and plate length play a significant role in the resonating pattern associated with the wave power generation curve. The results demonstrate that the PWEC device having moderate plate length and with free and moored type front edges generates a higher amount of wave power for a wider range of incident wave frequencies.

Effect of Trapezoidal Shapes on the Thermal Buckling Behaviour of Perforated Composite Plates

Abstract Thermal buckling study on the symmetric laminated composite trapezoidal plate with a circular cutout subjected to a uniform increase in temperature for various boundary conditions is explored in this paper. In a mathematical model, the first-order shear deformation principle is employed in accordance with the variational energy system. For acquiring the thermal buckling temperature, a nine-node heterosis plate relation has been used in the finite element formulation. By correlating the present findings with accessible literature, the effectiveness of the present formulation is verified. The impact of different parameters, such as trapezoidal shape, cutout size, ply-orientation, plate edge conditions and plate width to thickness ratio have been considered to study the effect of each parameters on the buckling characteristics of plate under various temperatures. It is observed from the study that each parametric investigation significantly affect the thermal buckling behaviour of trapezoidal plates.

Influence of Trapezoidal Shapes and Cutout Sizes on the Buckling Behaviour of Composite Laminates Under Thermally Induced Loads

Trapezoidal laminated plates with cutouts are commonly found in many engineering field, especially in aerospace structures. In many cases these plates are subjected to various harsh environmental conditions during its service life. Thermally induced load is the one which seriously affect the buckling characteristics of the structural components. The study presents the effect of rise in temperature on the thermal buckling characteristics of trapezoidal laminated composite plates with and without cutouts by using finite element technique. In order to model the plate, a 9-noded heterosis plate element has been used by incorporating the effect of shear deformation. By correlating present findings with the available literature, the effectiveness of the present formulation is verified. The computer program FORTRAN language has been developed to investigate the effect of different parameters such as trapezoidal shapes, cutout offsets, plate aspect ratio, ply-orientations, different thickness and plate edge conditions. The influence of each parameter on the thermal buckling behavior is well investigated through this work.

Buckling and free vibration analysis of piezoelectric laminated composite plates using various plate deformation theories

A finite strip method was developed for buckling and free vibration analysis of piezoelectric laminated composite plates based on various plate theories such as Zigzag, Refined plate and other higher order shear deformation theory by variation of transverse shear strains through plate thickness in the form of parabolic, sine and exponential. The plate edge conditions are considered to be simply supported and the polynomial shape functions are used to evaluate the in–plane and out–of–plane deflection and rotation of the normal cross section of plates in transverse direction. Numerical results were obtained based on various shear deformation plate theories to verify the proposed method. The effects of length to thickness ratio and fiber orientation of cross–ply and angle–ply laminate were presented. Also, the effect of different electrical conditions on the critical buckling load under in–plane forces and strains is investigated and electrical buckling load and natural frequency of piezoelectric laminate composite plates are calculated through numerical examples. In addition, the new results on the effect of piezoelectric layers thickness, placement of piezoelectric layers and also the effect of length to thickness ratio in the interaction of biaxial in–plane loading on critical buckling load were studied.

Oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography

On the basis of a potential theory and Euler-Bernoulli beam theory, an analytical solution for oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography is developed using matched eigenfunction expansions. Different from previous studies, the effects of a wave incident angle, a plate draft, three different plate edge conditions (free, simply supported and built-in) and a sea-bottom topography are all taken into account. Moreover, the plate edge conditions are directly incorporated into linear algebraic equations for determining unknown expansion coefficients in velocity potentials, which leads to a simple and efficient solving procedure. Numerical results show that the convergence of the present solution is good, and an energy conservation relation is well satisfied. Also, the present predictions are in good agreement with known results for special cases. The effects of the wave incident angle, the plate draft, the plate edge conditions and the sea-bottom topography on various hydrodynamic quantities are analyzed. Some useful results are presented for engineering designs.

Experimental evaluation of bolt pull-through in pultruded glass-fibre-reinforced polymer plate

An experimental investigation of the bolt pull-through stiffness and strength of pultruded glass-fibre-reinforced polymer (GFRP) plate is described. Details of an adjustable bolt pull-through test rig are presented. The rig was used to carry out 80 low and ultimate load tests on single bolts loaded in tension at the centres of square pultruded GFRP plates. In the tests, one plate thickness, two bolt diameters, four plate side lengths, two sets of plate edge conditions and two orientations of the principal orthotropic axes with respect to one of the edge conditions were investigated. Transverse stiffnesses as well as damage and ultimate tensile loads of the bolt–plate specimens were quantified from the test data. The latter are presented graphically to illustrate the effects of bolt diameter, plate slenderness, plate edge conditions, etc. on stiffnesses and damage/ultimate loads. Failure modes are also described and illustrated.

Applicability of the method of fundamental solutions to interaction of fully nonlinear water waves with a semi-infinite floating ice plate

Abstract In this research effort, a meshless numerical model was developed to study the hydroelastic interaction of an incident wave with a semi-infinite horizontal floating plate. It is assumed that the fluid is homogenous, inviscid and incompressible. Fundamental solution of the governing Laplace equation is considered to be radial basis functions. In this method, only a few boundary points are located on the boundary. Moreover, there are a few source points that are located outside the computational domain. Two additional source points are introduced to deal with the plate's edge conditions. The problem is solved using collocations at only a few boundary points. When density and thickness of the plate are reduced to zero, good agreements with other numerical works are observed.

Thermal and Geometrically Nonlinear Stress Analyses of an Adhesively Bonded Composite Tee Joint with Double Support

Carbon fiber reinforced plastics (CFRP) can be successfully joined to metal or composite structural components using the adhesive bonding technique [Semerdjiev, S. (1970). Metal to Metal Adhesive Bonding, Business Books Ltd., London.]. The stress and deformation fields occurring in the adhesive joints due to the thermal loads as well as the structural loads play an important role on the joint strength since the thermal and mechanical properties of the adhesive and adherends are different. Previous thermal stress analyses of the adhesive single-lap joints with simple geometries assumed a uniform temperature distribution through the adhesive joint, consequently predicted uniform thermal strain and stress distributions. In this study, the thermal stress analysis of an adhesively bonded tee joint with double support made of unidirectional CFRP was carried out for variable thermal loading conditions along its outer boundaries and different plate edge conditions. The large displacement and rotation effects were considered using the small strain-large displacement theory. The stress fields in the adhesive layer and the composite members of two tee joints bonded to a rigid base and a flexible plate were investigated. In the thermal analysis, a reference uniform temperature was attributed to all joint members for its stress free state, and air streams with different temperature and velocity were specified along the outer surfaces of the adhesive joint. In addition, the air streams were specified in the vertical or horizontal directions to the composite plates and adhesive layer. The consideration of convective and conductive heat transfer showed that nonuniform temperature distributions occurred in the adhesive tee joints. High heat fluxes took place along the free surfaces of the adhesive fillets at the free ends of the adhesive layers. Geometrical nonlinear stress analyses of two tee joints were carried out using the calculated temperature fields for two different plate edge conditions. Since the adhesive joints consist of materials with different thermal and structural properties, the thermal strains become incompatible along the adhesive layer–plate interfaces. Consequently, the stress concentrations occurred inside the adhesive fillets around the adhesive free ends, and in the regions near the adhesive layer–composite plate interfaces. The adhesive fillets, middle region of the horizontal plate, the elbow sections of the left and right supports appeared as most critical regions of the tee joints. In addition, the support length did not have similar effect of reducing the normal and shear stresses at these critical adhesive and adherend locations.

Thermal non-linear elastic stress analysis of an adhesively bonded T-joint

Adhesive joints consist of adherends and an adhesive layer having different thermal and mechanical properties. When they are exposed to uniform thermal loads the mechanical-thermal mismatches of the adherends and adhesive layer result in uniform but different thermal strain distributions in the adhesive and adherends. The thermal stresses arise near and along the adherend-adhesive interfaces. The present thermal stress analyses of adhesively bonded joints assume a uniform temperature distribution or a constant temperature imposed along the outer boundaries of adhesive lap joints. This paper outlines the thermal analysis and geometrically non-linear stress analysis of adhesive joints subjected to different plate edge conditions and varying thermal boundary conditions causing large displacements and rotations. In addition, the geometrically non-linear thermal stress analysis of an adhesively bonded T-joint with single support plus angled reinforcement was carried out using the incremental finite element method, which was subjected to variable thermal boundary conditions, i.e. air streams with different temperatures and velocities parallel and perpendicular to its outer surfaces. The steady state heat transfer analysis showed that the temperature distribution through the joint members was non-uniform and high heat fluxes occurred inside the adhesive fillets at the adhesive free ends. Based on the geometrically non-linear stress analysis of the T-joint bonded to both rigid and flexible bases for different plate edge conditions, stress concentrations were observed at the free ends of adhesive-adherend interfaces and inside the adhesive fillets around the adhesive free ends, and the horizontal and vertical plates also experienced considerable stress distributions along outer surfaces. In addition, the effect of support length on the peak thermal adhesive stresses was found to be dependent on the plate edge conditions, when a support length allowing moderate adhesive stresses was present.

Steady-state thermal and geometrical non-linear stress analysis of an adhesively bonded tee joint with double support

The adhesive joints consist of adhesive layer and adherends with different mechanical and thermal properties. In case the adhesive joint is subjected to a temperature difference, thermal stresses arise in the adhesive joint due to the thermal and mechanical mismatches of the adhesive layer and the adherends. If the thermal expansion of the adhesive joint is restrained the stresses in the adhesive and adherends can reach considerable levels. In this study, the geometrically non-linear thermal stress analysis of an adhesively bonded tee joint with double support was carried out using the finite element method. The configurations of the adhesive tee joint bonded to a rigid base and to a flexible horizontal plate were considered. It was assumed that the adhesive tee joint is subjected to variable thermal boundary conditions, that is, air flows with different temperature and velocity parallel and perpendicular to outer surfaces of the tee joint. In order to determine the thermal strains with respect to a reference temperature, it is necessary to know the final temperature distributions through the adhesive tee joint. The heat transfer analysis of the tee joint showed that high heat fluxes occurred inside the adhesive fillets at the adhesive free ends whereas the vertical and horizontal plates experience uniform low-temperature distributions. Based on the final temperature distribution of the adhesive tee joint its geometrical non-linear stress analysis was carried out considering large displacement effects for two plate edge conditions in which the edges of the vertical and horizontal plates were fully or partly constrained. The stress analyses showed that high stress concentrations occurred inside the adhesive fillets around the adhesive free ends. The surfaces of the vertical and horizontal plates near the free ends of the adhesive–plate interfaces and the adhesive–support interfaces also experience stress concentrations. The adhesive tee joint was subjected to the highest stresses in the adhesive layer and plates when the edges of the horizontal and vertical plates were fully fixed. In addition, increasing the effect of the support length resulted in increases in the peak stresses at the critical locations of the adhesive layer and the plates.

Wave structure in the radial film flow with a circular hydraulic jump

A circular hydraulic jump is commonly seen when a circular liquid jet impinges on a horizontal plate. Measurements of the film thickness, jump radius and the wave structure for various jet Reynolds numbers are reported. Film thickness measurements are made using an electrical contact method for regions both upstream and downstream of the jump over circular plates without a barrier at the edge. The jump radius and the separation bubble length are measured for various flow rates, plate edge conditions, and radii. Flow visualization using high-speed photography is used to study wave structure and transition. Waves on the jet amplify in the film region upstream of the jump. At high flow rates, the waves amplify enough to cause three-dimensional breakdown and what seems like transition to turbulence. This surface wave induced transition is different from the traditional route and can be exploited to enhance heat and mass transfer rates.

A class of expansion functions for finite elastic plates in structural acoustics

Problems in structural acoustics involving finite plates can be formulated using integral equation methods. The unknown function within the integral equation must satisfy the plate edge conditions, and hence appropriate expansion functions must be used. The expansion functions developed here are aimed at treating a wide class of problems. Once such functions are found, the solution process and numerical implementation are relatively straightforward. The speed of convergence to “exact” comparison solutions is fast even in the singular limit of high frequencies and wide plates. A set of expansion functions with the required properties is constructed and some illustrative problems are treated.

The effect of mean flow on the radiation efficiency of rectangular plates

The acoustic power radiated by a rectangular plate bounded by a uniform mean flow is investigated. Asymptotic expressions for the modal radiation efficiency of a simply supported plate are derived, and confirmed by comparison with numerical results. The asymptotic expressions show that the frequency at which a mode becomes an efficient radiator is reduced in the presence of mean flow, and hence that the critical frequency for a vibrating elastic plate is similarly lowered. The effects of these changes on the radiation damping of an aircraft panel in cruise, and on its radiation efficiency on landing, are investigated. The asymptotic results are then extended to more general plate edge conditions via analysis of appropriate infinite and semi–infinite problems. Hence the ‘3 dB rule’, that a plate with clamped edges, vibrating well below the critical frequency, radiates twice the power of a plate with simple supports, is shown to apply also in the presence of mean flow.

Large deflection initial failure analysis of angle-ply laminated plates

A large deflection initial failure analysis of square angle-ply laminated plates subjected to uniform pressure loading is described. Approximate numerical solutions of the Mindlin laminated plate equations are derived using finite differences in conjunction with the Dynamic Relaxation (DR) technique. The solutions are scaled to satisfy the Tsai-Hill lamina failure criterion. The effects of plate slenderness, in-plane edge restraint and lay-up on the initial failure pressure and associated plate centre deflection are quantified for ±45° laminated plates with simply supported and clamped edges. It is shown, particularly for thin plates, that in-plane edge restraint increases the initial failure pressure substantially, though changing the plate edge conditions from simply supported to clamped does not always increase the initial failure pressure.

Flexural vibration of symmetrically laminated composite rectangular plates including transverse shear effects

The flexural vibration of symmetrically laminated rectangular plates is considered, based upon the adoption of a shear-deformation plate theory. This theory is an extension of Mindlin's theory for isotropic plates and includes the effects of both transverse shear deformation and rotary inertia. Two related methods of analysis are described, namely the Rayleigh-Ritz method and the finite-strip method. The assumed displacement fields incorporate the use of the normal modes of vibration of Timoshenko beams and arbitrary combinations of standard plate edge conditions are accommodated. Results presented for orthotropic simply supported plates show very close comparison with available exact results of three-dimensional elasticity theory, when appropriate selection of shear correction factors is made. A range of results is presented for orthotropic square plates with various combinations of boundary conditions, and these results serve to demonstrate both the convergence qualities of the solution procedures and the very large errors that can be associated with analyses based upon the use of the classical plate theory. A final numerical study is concerned with a clamped anisotropic plate and reveals, not unexpectedly, that convergence of results is less rapid than it is for corresponding orthotropic plates.

The vibration and stability of symmetrically-laminated composite rectangular plates subjected to in-plane stresses

Consideration is given to the twin problems of the elastic buckling of rectangular, symmetrically-laminated composite plates and of the vibration in the presence of applied in-plane stress of such laminates. First-order shear deformation plate theory provides the mathematical model of plate behaviour and the Rayleigh-Ritz and finite strip methods are used to generate numerical results for laminates of thin and moderately thick geometry, with various combinations of standard plate edge conditions. The applied stresses include uniform shear stress as well as direct stresses, and anisotropic material properties can be included. The presented results demonstrate the accuracy of the numerical methods and highlight the very significant influence that transverse shear and related thickness effects can have in the subject problems.