An Invariant Analysis of the Bending of Three Edge-Bonded Dissimilar Plates

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
K. Aderogba
Keyword(s):  
Parallel Plate ◽  
Isotropic Plate ◽  
Bending Moments ◽  
Vertical Load ◽  
Effective Elastic Constants ◽  
Isotropic Plates ◽  
Plate Strip ◽  
Finite Breadth ◽  
Invariant Analysis ◽  
Compound Plate

A representation theorem is proved for the solution of the problem of two perfectly bonded isotropic semi-infinite plates under the influence of an arbitrary vertical load located in the midplane of the interior of one of them. Its function is to show that if the deflection of an unbounded isotropic plate under the influence of an arbitrary vertical load is known, then the corresponding deflections for two perfectly bonded isotropic semi-infinite plates are explicitly determinable, solely, and compactly in terms of the known deflection. Indeed, whatever the nature of the mechanism of loading is, the induced bending moments and shears in the two bonded plates are determinable by the process of differentiation only. A systematic repeated application of the theorem then yields a well-structured series solution when the arbitrary vertical load is arbitrarily located in a compound plate comprising two semi-infinite dissimilar isotropic plates separated by another dissimilar isotropic plate strip of finite breadth. As an application, we determine the effective elastic constants of a compound plate comprising a homogeneous isotropic plate in which a finite number of isotropic parallel plate strips of small breadths are embedded at such distances apart that their interaction effects may be taken as independent of one another.

Analysis of Stress Singularities at Bi-Material Corners in Reddy's Theory of Plate Bending

2006 ◽  
Vol 22 (1) ◽  
pp. 67-75 ◽  
Author(s):  
C. S. Huang
Keyword(s):  
Thick Plate ◽  
Isotropic Plate ◽  
Plate Theory ◽  
Stress Singularity ◽  
Numerical Approach ◽  
Sharp Corner ◽  
Equilibrium Equations ◽  
Third Order ◽  
Isotropic Plates ◽  
Expansion Technique

AbstractThe order of stress singularity at a sharp corner of a plate needs to be known before a numerical approach can be taken to determine accurately the stress distribution of a plate with irregular geometry (such as a V-notch) under loading. This work analyzes the order of the stress singularity at a bi-material corner of a thick plate under bending, based on Reddy's third-order shear deformation plate theory. An eigenfunction expansion technique is used to derive the asymptotic displacement field in the vicinity of the sharp corner by solving the equilibrium equations in terms of displacement functions. This paper explicitly shows the first known characteristic equations for determining the order of the stress singularity at the interface corner of a bonded dissimilar isotropic plate. Moreover, the numerical results are given in graphic form for the order of stress singularity at the interface corner in bonded dissimilar isotropic plates and at the vertex of a bi-material wedge with free radial edges. The results presented herein fill some of the gaps in the literature

Displacement States for Isotropic Plates

2018 ◽  
Vol 16 (14) ◽  
pp. 64-67
Author(s):  
Carmen Popa ◽  
Violeta Anghelina ◽  
Octavian Munteanu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Isotropic Plate ◽  
The Finite Element Method ◽  
Isotropic Plates ◽  
Deformation State ◽  
Element Method

Abstract In this paper the deformation state of a circular and isotropic plate is analyzed, using as methods of comparison the analytical, the finite element and the experimental element methods. In the finite element method, the plate is analyzed by several programmes, as well as assembled with the respective container.

Cumulative Second Harmonics in a Nonlinear Transversely Isotropic Plate

2015 ◽  
Author(s):  
Jinling Zhao ◽  
Vamshi K. Chillara ◽  
Hwanjeong Cho ◽  
Jinhao Qiu ◽  
Cliff J. Lissenden
Keyword(s):  
Isotropic Plate ◽  
Second Harmonic ◽  
Strain Tensor ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Guided Wave ◽  
Power Flux ◽  
Weakly Nonlinear ◽  
Isotropic Plates ◽  
Transversely Isotropic Plate

The problem of second harmonic guided wave generation in transversely isotropic plates is investigated from a theoretical and numerical standpoint. The strain energy function of transversely isotropic materials is written down using five invariants in terms of the Green-Lagrange strain tensor and contains five linear terms and nine nonlinear terms. Theoretical investigations reveal that second harmonics in a weakly nonlinear transversely isotropic plate are cumulative only when the phase matching and nonzero power flux criteria are satisfied. Also, only cumulative secondary symmetric Lamb wave modes can be generated — a conclusion in line with what is observed for isotropic plates. Finally, numerical simulations are carried out to examine the cumulative second harmonic generation from the S0 mode and the results obtained are discussed in the light of the theory.

Development of a parametric model for the prediction of concrete railway crosstie service bending moments

2019 ◽  
Vol 234 (10) ◽  
pp. 1253-1264
Author(s):  
J Riley Edwards ◽  
Yubing Liang ◽  
Josué C Bastos ◽  
Marcus S Dersch
Keyword(s):  
Concrete Surface ◽  
Parametric Model ◽  
Surface Strain ◽  
Strain Gauges ◽  
Rail Transit ◽  
Bending Moments ◽  
Vertical Load ◽  
Support Condition ◽  
Reliable Model ◽  
Railroad Applications

Concrete crosstie usage in North America continues to increase for rail transit and heavy axle load freight railroad applications. As such, it is important to design optimized crossties to save both capital and maintenance funds. Recently, a method for quantifying concrete crosstie bending moments using concrete surface strain gauges has been developed, deployed, and validated. Data from this method are used in this paper for (1) building a model to quantify sources of variability for field bending moments and the relative influence of each source, (2) generating an accurate model to predict bending moments at the two field locations surveyed, and (3) comparing the relative effects of predictor variables on rail transit and heavy axle load freight rail modes to determine their influence on service bending moments. Results show that it is possible to develop a reliable model to predict bending moments, and that several factors have a strong influence on these predictions, namely vertical load, temperature gradient, and axle location within a railcar truck. The most significant factor is the crosstie support condition, especially with respect to center moments. While the aforementioned model’s primary utility is for the two sites and railroad systems surveyed, the model provides a valuable tool for determining which variables are the most critical for inclusion in the future mechanistic design of concrete crossties.

scholarly journals The transverse flexure of perforated isotropic plates

1946 ◽  
Vol 185 (1000) ◽  
pp. 35-49 ◽  
Keyword(s):  
General Solution ◽  
Isotropic Plate ◽  
Theoretical Solution ◽  
General Shape ◽  
Stress Couple ◽  
Isotropic Plates ◽  
Special Cases ◽  
Square Hole

A general theoretical solution is obtained for the problem of a large thin isotropic plate bent or twisted by couples at infinity, and containing a hole of fairly general shape. Certain known results for circular and elliptical boundaries are included in this general solution as special cases. Numerical values of the stress couple round the edge of a square hole with rounded comers are given when the plate is bent by all-round couples, or twisted or bent cylindrically about the diagonals or sides of the square. Results are also given for a triangular hole with rounded corners in a plate subject to the action of similar distributions of stress -couple at infinity.

scholarly journals Study of the Force and Deformation Characteristics of Subsea Mudmat-Pile Hybrid Foundations

2018 ◽  
Vol 25 (s3) ◽  
pp. 43-53 ◽  
Author(s):  
Desen Kong ◽  
Meixu Deng ◽  
Yi Liu ◽  
Xiaoyan Tan
Keyword(s):  
Bending Moment ◽  
Simulation Software ◽  
Horizontal Load ◽  
Deformation Characteristics ◽  
Bending Moments ◽  
Vertical Load ◽  
Pile Shaft ◽  
Combined Loads ◽  
Moment Load ◽  
Seabed Soil

Abstract To study the force and deformation characteristics of subsea mudmat-pile hybrid foundations under different combined loads, a project at a water depth of 200 m in the South China Sea was studied. A numerical model of a subsea mudmatpile hybrid foundation is developed using the numerical simulation software FLAC3D. The settlement of the seabed soil, the bending moments of the mudmat, and the displacements and bending moments along the pile shaft under different load combinations, including vertical load and horizontal load, vertical load and bending moment, and horizontal load and bending moment load, are analyzed. The results indicate that settlement of the seabed soil is reduced by the presence of piles. The settlement of the mudmat is reduced by the presence of piles. Different degrees of inclination occur along the pile shaft. The angle of inclination of pile No. 1 is greater than that of pile No. 2. The dip directions of piles No. 1 and No. 2 are identical under the vertical load and bending moment and are opposite to those under the other combined loads. The piles that are located at the junctions between the mudmat and the tops of the piles are easily destroyed.

BUCKLING AND FREE VIBRATION BEHAVIOR OF AN ISOTROPIC PLATE UNDER NONUNIFORM THERMAL LOAD

2013 ◽  
Vol 13 (03) ◽  
pp. 1250071 ◽  
Author(s):  
P. JEYARAJ
Keyword(s):  
Free Vibration ◽  
Thermal Field ◽  
Isotropic Plate ◽  
Free Edge ◽  
Maximum Temperature ◽  
Vibration Modes ◽  
Simulation Studies ◽  
Buckling Mode ◽  
Nodal Lines ◽  
Isotropic Plates

This paper presents numerical simulation studies on buckling and free vibration characteristics of isotropic plates under arbitrarily varying temperature distributions using finite element method (FEM). First the critical buckling temperature is obtained, followed by modal analysis considering pre-stress due to the thermal field in the plate, with the critical buckling temperature as a parameter. It is found that anti-nodal position of the fundamental buckling mode appears away/near to the free edge when the free edge is exposed to minimum/maximum temperature of the variation. The nodal and anti-nodal lines of free vibration modes moves towards the high temperature exposed plate and nodal lines becomes a nodal area for longer plates.

Foundation Slab in Interaction with Subsoil

2013 ◽  
Vol 838-841 ◽  
pp. 375-380 ◽  
Author(s):  
Radim Čajka ◽  
Kamil Burkovič ◽  
Vojtech Buchta
Keyword(s):  
Fem Analysis ◽  
Plain Concrete ◽  
Bending Moments ◽  
Vertical Load ◽  
Foundation Slab

In the paper the experiment results of deformation in foundation slab segment in interaction with subsoil are presented. Pilot measurement is carried out on original subsoil with characteristics which were tested in cooperation with geotechnics specialists. Concrete precast slab with square dimensions 500 mm and with thickness 48 mm made of plain concrete is exposed to vertical load. The tests results are compared with bending moments and deformations analysed according to subsoil models given in Eurocodes using FEM analysis.

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