Some New Types of Orthotropic Plates Laminated of Orthotropic Material

1953 ◽  
Vol 20 (2) ◽  
pp. 286-288
Author(s):  
C. Bassel Smith
Keyword(s):  
Plane Stress ◽  
Orthotropic Material ◽  
Laminated Plates ◽  
The Other ◽  
Arbitrary Angle ◽  
Orthotropic Plates ◽  
Elastic Symmetry

Abstract Plywood plates are usually constructed so that the grain of adjacent plies is perpendicular. Such laminated plates possess two perpendicular axes of elastic symmetry. In this discussion plywood plates having other than 90 degree angles between the grain of adjacent plies are considered. First, a two-ply plate with the grain of one ply making any arbitrary angle with the grain of the other ply is discussed. It is shown that this plate, when in a state of plane stress or when subjected to small deflections, possesses the same two perpendicular axes of elastic symmetry. By making use of the formulas obtained for the two-ply plate, it is shown how to construct a plate of any number of plies (the adjacent plies not necessarily having their grain perpendicular) possessing the same type of elastic symmetry as the two-ply plate.

The Affine Transformation for Orthotropic Plane-Stress and Plane-Strain Problems

1956 ◽  
Vol 23 (1) ◽  
pp. 1-6
Author(s):  
H. A. Lang
Keyword(s):  
Shear Modulus ◽  
Plane Strain ◽  
Elastic Constants ◽  
Plane Stress ◽  
Affine Transformation ◽  
Orthotropic Material ◽  
Elastic Symmetry ◽  
Concentrated Load ◽  
Plane Strain Problem ◽  
Orthotropic Plane

Abstract It is demonstrated that a single affine transformation of the type x = ax′, y = by′ immediately extends the solution of any isotropic plane-stress or plane-strain problem to the solution of an orthotropic plane problem where the orthotropic material is characterized by three independent constants. Since orthotropy, defined as elastic symmetry with respect to two orthogonal axes, implies four independent elastic constants, the affine transformation introduces a restriction upon the orthotropic shear modulus. The orthotropic shear modulus differs from that used by previous investigators. This difference alters the equation which the orthotropic stress function must satisfy and, therefore, directly affects the solution to every plane-stress or plane-strain problem. Some arguments are advanced to favor the shear modulus, as here defined, whenever orthotropy must be restricted to three elastic constants. The two solutions of the orthotropic half plane subjected to a normal concentrated load are contrasted to illustrate the effect of the two definitions of orthotropic shear modulus.

Orthotropic Characteristics of Glass-Fibre-Epoxy Laminates under Plane Stress

1973 ◽  
Vol 15 (2) ◽  
pp. 102-108 ◽  
Author(s):  
R. M. Ogorkiewicz
Keyword(s):  
Tensile Strength ◽  
Epoxy Resin ◽  
Uniaxial Tension ◽  
Plane Stress ◽  
Glass Fibre ◽  
Orthotropic Material ◽  
Glass Fibres ◽  
Degree Of Anisotropy

Deformational characteristics of laminates of unidirectionally arranged glass fibres and epoxy resin under plane stress are shown to correspond very closely under uniaxial tension and, to a lesser extent, under shear to the theroetical pattern of stiffness of an orthotropic material. The anisotropy in stiffness is also shown to be accompanied by an even greater degree of anisotropy in tensile strength.

A Numerical Approach for Simulation of Rock Fracturing in Engineering Blasting

2012 ◽  
pp. 203-224
Author(s):  
Mani Ram Saharan ◽  
Hani Mitri
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modelling ◽  
Knowledge Base ◽  
Plane Stress ◽  
Numerical Approach ◽  
The Other ◽  
Brittle Rock ◽  
Rock Fracturing ◽  
Element Elimination

An approach for simulation of rock fracturing as a result of engineering blasting is presented in this paper. The approach uses element elimination technique within the framework of finite element method to capture the physics of engineering blasting. The approach does not require pre-placement of fracture paths which is the severe drawback of the other existing methodologies and approaches. Results of plane stress modelling for isotropic brittle rock behaviour are presented in this paper and these results are in good agreement with the existing knowledge base. The authors also review the existing approaches of numerical modelling to compare the efficacy of the element elimination technique. It is anticipated that the further developments with this approach can prove to be good experimental tool to improve engineering blasting operations.

Spectral Fatigue Analysis of Plate Surface Hot-Spots: A Practical Solution to the Stress Direction Issue

2020 ◽  
Author(s):  
Fabien Bigot ◽  
Stéphanie Mougin
Keyword(s):  
Finite Element ◽  
Spectral Analysis ◽  
Fatigue Strength ◽  
Plane Stress ◽  
Hot Spots ◽  
Fatigue Analysis ◽  
Multiaxial Fatigue ◽  
The Other ◽  
Plate Surface ◽  
Practical Solution

Abstract Spectral Fatigue Analysis using coupled hydrodynamics and finite element models has now become a common practice for the fatigue strength assessment of offshore units, with established procedures given in Classification Rules. However, users are facing a practical issue that is almost never mentioned in the procedures. Indeed, many fatigue hot-spots are located on a plate surface, as opposed to plate edges. For such hot-spots, the finite element model results are the three components of the plane-stress stress tensor. Therefore, the outcome of the Spectral Fatigue Analysis is a set of three transfer functions (RAOs). On the other hand, our industry’s practice regarding the fatigue strength model is still the proven « design S-N curve » approach in combination with the Palmgren-Miner’s damage summation. As a consequence, today the engineer is left with no clear instruction about the proper way how to close this gap between the three stress RAOs on the one hand, and the single stress S-N curve on the other hand. If any advice is given, it is most often to consider the principal stresses, tentatively extending to spectral analysis the classification rule load cases approach. However, principal stress determination is a non-linear procedure that is not compatible with spectral analysis in frequency domain. Turning the spectral results into time domain to overcome this limitation is extremely costly and is not straightforward. Of course, a rational solution to this issue would be the adoption of a multiaxial fatigue damage criteria in lieu of the uniaxial S-N curve. But until such a multiaxial fatigue criteria is widely accepted in our industry, users have to square the circle, and force their stress tensor RAOs into the existing rule criteria. In this paper, a practical solution to reconcile plane stress results and conventional S-N curve criterion in spectral fatigue is proposed: the “facet approach “.

Anisotropic Plates With Various Openings Under Uniform Loading or Pure Bending

1990 ◽  
Vol 57 (3) ◽  
pp. 700-706 ◽  
Author(s):  
Chyanbin Hwu
Keyword(s):  
Approximate Solution ◽  
Stress Concentration ◽  
Hoop Stress ◽  
Anisotropic Plate ◽  
The Other ◽  
Real Form ◽  
Orthotropic Plates ◽  
Pure Bending ◽  
Uniform Loading ◽  
Anisotropic Plates

In the case when an anisotropic plate contains a triangular, oval, or square opening, the only solution available in the literature is an approximate solution for orthotropic plates with openings, which was obtained by Lekhnitskii using the complex variable formulation. Solutions for any kind of anisotropic plates with various openings are presented in this paper by applying the Stroh formalism and using the technique of conformal mapping. Unlike the former results, which have different orders of approximation for different openings, the solutions presented here have only one simple unified expression for various openings such as the ellipse, circle, crack, triangle, oval, and square. Two special loading conditions are considered: one is uniform loading, the other is pure bending. Through the use of identities developed in the literature, the hoop stress along the opening boundary is obtained in real form. The results show that the effect of anisotropy on the stress concentration is totally determined through the fundamental elasticity matrices N1 and N3 introduced by Stroh.

Reflection of Dilatational Waves at the Edge of a Plate

1957 ◽  
Vol 24 (2) ◽  
pp. 219-227
Author(s):  
T. R. Kane
Keyword(s):  
Shear Wave ◽  
Plane Stress ◽  
Plate Theory ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Arbitrary Angle ◽  
Reflected Waves ◽  
Dilatational Wave ◽  
Special Cases

Abstract The reflection of straight-crested dilatational waves at the edge of a semi-inflnite plate is studied in terms of a two-dimensional plate theory and in terms of the theory of generalized plane stress. It is found that, in general, a dilatational wave propagated toward the edge at an arbitrary angle of incidence gives rise to three reflected waves; namely, two dilatational waves and a shear wave. A number of special cases are investigated in detail.

Bending and Stretching of Certain Types of Heterogeneous Aeolotropic Elastic Plates

1961 ◽  
Vol 28 (3) ◽  
pp. 402-408 ◽  
Author(s):  
E. Reissner ◽  
Y. Stavsky
Keyword(s):  
The Other ◽  
Explicit Solutions ◽  
Elastic Plates ◽  
Important Special Case ◽  
Elastic Symmetry ◽  
Transverse Bending ◽  
Special Case ◽  
Equal Thickness

The class of plates with which this paper is concerned includes as an important special case plates consisting of two orthotropic sheets of equal thickness which are laminated in such a way that the axes of elastic symmetry enclose an angle +θ with the x, y-axes in one sheet and an angle −θ in the other sheet. For plates of this type there occurs a coupling phenomenon between in-plane stretching and transverse bending which does not occur in the theory of homogeneous plates and which has not been considered in earlier work for such plates. The general results of the present paper are illustrated by means of explicit solutions for two specific plate problems.

The Large Deflection and Post-Buckling Behaviour of Some Laminated Plates

1973 ◽  
Vol 24 (2) ◽  
pp. 77-86 ◽  
Author(s):  
G J Turvey ◽  
W H Wittrick
Keyword(s):  
Large Deflection ◽  
Middle Surface ◽  
Laminated Plates ◽  
Dynamic Relaxation ◽  
Orthotropic Plates ◽  
Stability Problems ◽  
Linear Elastic ◽  
Dr Method ◽  
Post Buckling ◽  
Coupling Phenomena

SummaryThe Dynamic Relaxation (DR) method is applied to the solution of geometrically non-linear, elastic, laminated plate, flexural and stability problems. Two categories of plate are considered, namely, those that are symmetrically and unsymmetrically laminated with respect to the plate middle surface. Whereas the former category exhibits a bending – twisting coupling phenomenon, the latter exhibits an extensional – flexural type of coupling. The effects of these coupling phenomena are evaluated by comparing the plate responses with those of corresponding homogeneous, specially orthotropic plates. With the exception of uniaxially compressed plates of the latter category in the post-buckling regime, it is found that for both flexural and stability problems the coupling phenomena cause a reduction in stiffness and the extent of this reduction is dependent on the lay-up of the laminate.

A Numerical Approach for Simulation of Rock Fracturing in Engineering Blasting

2010 ◽  
Vol 1 (2) ◽  
pp. 38-58
Author(s):  
Mani Ram Saharan ◽  
Hani S. Mitri
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modelling ◽  
Plane Stress ◽  
Numerical Approach ◽  
The Other ◽  
Rock Fracturing ◽  
Experimental Tool ◽  
Element Elimination ◽  
Good Agreement

An approach for simulation of rock fracturing as a result of engineering blasting is presented in this paper. The approach uses element elimination technique within the framework of finite element method to capture the physics of engineering blasting. The approach does not require pre-placement of fracture paths which is the severe drawback of the other existing methodologies and approaches. Results of plane stress modelling for isotropic brittle rock behaviour are presented in this paper and these results are in good agreement with the existing knowledge base. The authors also review the existing approaches of numerical modelling to compare the efficacy of the element elimination technique. It is anticipated that the further developments with this approach can prove to be good experimental tool to improve engineering blasting operations.

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