End Effects in Laminated Anisotropic Beams — Part I

1995 ◽  
Vol 117 (4) ◽  
pp. 279-284
Author(s):  
J. A. Ackermann ◽  
T. J. Kozik
Keyword(s):  
Stress Field ◽  
Normal Stress ◽  
Transverse Shear ◽  
Analytical Method ◽  
Normal Load ◽  
End Effects ◽  
Laminated Beam ◽  
Simply Supported ◽  
Combination Of Material

The derivation of an analytical method to examine the stress field near the end of a simply supported, laminated beam is presented. Specific effort has been directed to accurately calculate the transverse-shear and normal stress by incorporating the exact displacement relations derived, by Kozik (1970). The method accommodates any combination of material lay-up and any type of normal load on the upper and lower surfaces. The reactions at the ends of the beam may be distributed over the surface edges in a fashion most accurately characterizing the physical supports. The solution and application of the method is presented in Part II of this paper.

End Effects in Laminated Anisotropic Beams—Part II

1995 ◽  
Vol 117 (4) ◽  
pp. 285-289
Author(s):  
J. A. Ackermann ◽  
T. J. Kozik
Keyword(s):  
Normal Load ◽  
Analysis Procedure ◽  
Normal Stresses ◽  
Timoshenko Theory ◽  
End Effects ◽  
Laminated Beam ◽  
Analytical Technique ◽  
Simply Supported ◽  
Aluminum Beam ◽  
Combination Of Material

An analytical method of examining the stress field near the edge of a simply supported, laminated beam was developed in Part I of this paper. The result was a system of second-order, ordinary, linear, nonhomogeneous differential equations. A numerical and analytical technique for solving these equations is presented in this paper. The method is a versatile stress analysis procedure which can accommodate any combination of material lay-up and can simulate any prescribed distribution of normal load on the upper and lower surfaces. The reactions at the ends of the beam may be distributed over the surface edges in a fashion most accurately characterizing the physical supports. An all-steel lay-up is examined as a basis for comparison with Bernoulli-Euler and Timoshenko theory; and a two-layered steel/aluminum beam is examined to simply demonstrate the method’s capability of determining the interlaminar transverse shear and normal stresses.

Natural Frequency of Laminated Composite Plates Using a Sinusoidal Theory

2014 ◽  
Vol 709 ◽  
pp. 148-152
Author(s):  
Guo Qing Zhou ◽  
Ji Wang ◽  
Song Xiang
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Sinusoidal Shear Deformation Theory

Sinusoidal shear deformation theory is presented to analyze the natural frequencies of simply supported laminated composite plates. The governing differential equations based on sinusoidal theory are solved by a Navier-type analytical method. The present results are compared with the available published results which verify the accuracy of sinusoidal theory.

Analysis of the Elastic Contact of a Hollow Ball With a Flat Plate

1970 ◽  
Vol 92 (1) ◽  
pp. 138-142 ◽  
Author(s):  
J. H. Rumbarger ◽  
R. C. Herrick ◽  
P. R. Eklund
Keyword(s):  
Shear Stress ◽  
Stress Field ◽  
Flat Plate ◽  
Normal Load ◽  
Thick Wall ◽  
Elastic Contact ◽  
Solid Ball ◽  
Ball Contact ◽  
Contact Life ◽  
Hollow Ball

This paper presents the analysis of the stress field in a hollow sphere in the vicinity of the contact area. The sphere is subjected to a normal load applied through a flat plate. The elastic contact shape and extent are developed for a load of 1000 lb applied to a 1-in-dia hollow ball with a 0.08-in-thick wall. Hollow ball shell bending stresses have a significant effect upon the subsurface stress field. Fatigue life estimates for the hollow ball vary significantly depending upon the selection of decisive stress amplitude. Comparison of the maximum value and location of the reversing orthogonal subsurface shear stress with solid ball data according to the Lundberg-Palmgren dynamic life theory predicts a 91.6 percent life reduction for the hollow ball contact. The use of the unidirectional subsurface shear stress results in a prediction of hollow ball contact life over 30 times the solid ball contact life.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

The Behavior of a Poroelastic Seabed Under Normal and Shear Loads

1989 ◽  
Vol 111 (4) ◽  
pp. 303-310
Author(s):  
G. C. W. Sabin
Keyword(s):  
Normal Stress ◽  
Normal Load ◽  
Extended Period ◽  
Offshore Structures ◽  
Theoretical Discussion ◽  
Shear Loads ◽  
Pore Pressure Response ◽  
Limiting Case ◽  
Poroelastic Seabed ◽  
Parameters Of Interest

One of the effects of ice and water forces on large offshore structures which rest on the seabed is to transmit surface tractions to the region of contact. A recent paper by Sabin and Raman-Nair [1] has examined the effect of a normal axisymmetric load P(r, t) on a poroelastic seabed under several different conditions of boundary permeabilities. That study provided a number of general formulas for an arbitrary normal load. The present paper extends the results found in [1] to include shear tractions. While reference [1] was primarily a theoretical discussion, the present paper examines several specific forms of loading and presents graphs showing the normal stress and pore pressure response for various values of the parameters of interest. These results are compared with the limiting case of an extended period of time.

An Analytical Method for Static Analysis of Double Layer Grids

1989 ◽  
Vol 4 (2) ◽  
pp. 107-116 ◽  
Author(s):  
H.C. Chan ◽  
C.W. Cai ◽  
Y.K. Cheung
Keyword(s):  
Exact Solutions ◽  
Static Analysis ◽  
Double Layer ◽  
Analytical Method ◽  
Transformation Technique ◽  
Simply Supported ◽  
Axial Forces ◽  
Nodal Displacements

An analytical method for the static analysis of double layer grids consisting of diagonals and top and bottom layers which are plane orthogonal grids is presented. It is assumed that the double layer grid is simply supported at all nodes located at the boundary of the top layer. By using the double U-transformation technique, exact solutions for the nodal displacements and axial forces of the bars in the double layer grid can be derived. The validity of the method is demonstrated with a simple example.

Effects of In-plane Load on Flutter of Homogeneous Laminated Beam Plates with Delamination

2000 ◽  
Vol 123 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Le-Chung Shiau ◽  
Yuan-Shih Chen
Keyword(s):  
Mach Number ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Compressive Load ◽  
Two Dimensional ◽  
Plate Model ◽  
Laminated Beam ◽  
Simply Supported ◽  
Flutter Boundary ◽  
Homogeneous Beam

The effects of in-plane load on flutter characteristics of delaminated two-dimensional homogeneous beam plates at high supersonic Mach number are investigated theoretically. Linear plate theory and quasi-steady supersonic aerodynamic theory are employed. A simple beam-plate model is developed to predict the effects of in-plane load on flutter boundaries for the delaminated beam plates with simply supported ends. Results reveal that the presence of an in-plane compressive load degrades the stiffness and natural frequencies of the plate and thereby decreases the flutter boundary for the plate. However, for certain geometry, the flutter boundaries were raised due to flutter coalescence modes of the plate altered by the presence of the in-plane load on the plate.

Influence of Porosity on Plane Strain Tensile Crack-Tip Stress Fields in Elastic-Plastic Materials: Part I

1992 ◽  
Vol 59 (3) ◽  
pp. 559-567 ◽  
Author(s):  
W. J. Drugan ◽  
Y. Miao
Keyword(s):  
Stress Field ◽  
Closed Form ◽  
Normal Stress ◽  
Plane Strain ◽  
Plane Stress ◽  
Entire Range ◽  
Crack Tip ◽  
Constant Stress ◽  
Tensile Crack ◽  
Stress Discontinuity

We perform an analytical first study of the influence of a uniform porosity distribution, for the entire range of porosity level, on the stress field near a plane strain tensile crack tip in ductile material. Such uniform porosity distributions (approximately) arise in incompletely sintered or previously deformed (e.g., during processing) ductile metals and alloys. The elastic-plastic Gurson-Tvergaard constitutive formulation is employed. This model has a sound micromechanical basis, and has been shown to agree well with detailed numerical finite element solutions of, and with experiments on, voided materials. To facilitate closed-form analytical results to the extent possible, we treat nonhardening material with constant, uniform porosity. We show that the assumption of singular plastic strain in the limit as the crack tip is approached renders the governing equations statically determinate with two permissible types of near-tip angular sector: one with constant Cartesian components of stress (“constant stress”); and one with radial stress characteristics (“generalized centered fan”). The former admits an exact asymptotic closed-form stress field representation, and although we prove the latter does not, we derive a highly accurate closed-form approximate representation. We show that complete near-tip solutions can be constructed from these two sector types for the entire range of porosity. These solutions are comprised of three asymptotic sector configurations: (i) “generalized Prandtlfield”for low porosities (0 ≤ f ≤ .02979), similar to the plane strain Prandtl field of fully dense materials, with a fully continuous stress field but sector extents that vary with porosity; (ii) “plane-stress-like field” for intermediate porosities (.02979 < f < .12029), resembling the plane stress solution for fully dense materials, with a ray of radial normal stress discontinuity but sector extents that vary with porosity; (iii) two constant stress sectors for the remaining high porosity range, with a ray of radial normal stress discontinuity and fixed sector extents. Among several interesting features, the solutions show that increasing porosity causes significant modification of the angular variation of stress components, particularly for a range of angles ahead of the crack tip, while also causing a drastic reduction in maximum hydrostatic stress level.

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