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- Lame's_stress_ellipsoid abstract "Lame's stress ellipsoid (Figure coming) is an alternative to Mohr's circle for the graphical representation of the stress state at a point. The surface of the ellipsoid represents the locus of the endpoints of all stress vectors acting on all planes passing through a given point in the continuum body. In other words, the endpoints of all stress vectors at a given point in the continuum body lie on the stress ellipsoid surface, i.e., the radius-vector from the center of the ellipsoid, located at the material point in consideration, to a point on the surface of the ellipsoid is equal to the stress vector on some plane passing through the point. In two dimensions, the surface is represented by an ellipse (Figure coming).Once the equations of the ellipsoid is known, the magnitude of the stress vector can then be obtained for any plane passing through that point.To determine the equation of the stress ellipsoid we consider the coordinate axes taken in the directions of the principal axes, i.e., in a principal stress space. Thus, the coordinates of the stress vector on a plane with normal unit vector passing through a given point is represented byAnd knowing that is a unit vector we havewhich is the equation of an ellipsoid centered at the origin of the coordinate system, with the lengths of the semiaxes of the ellipsoid equal to the magnitudes of the principal stresses, i.e. the intercepts of the ellipsoid with the principal axes are . The first stress invariant is directly proportional to the sum of the principal radii of the ellipsoid. The second stress invariant is directly proportional to the sum of the three principal areas of the ellipsoid. The tree principal areas are the ellipses on each principal plane. The third stress invariant is directly proportional to the volume of the ellipsoid. If two of the three principal stresses are numerically equal the stress ellipsoid becomes an ellipsoid of revolution. Thus, two principal areas are ellipses and the third is a circle. If all of the principal stresses are equal and of the same sign, the stress ellipsoid becomes a sphere and any three perpendicular directions can be taken as principal axes.The stress ellipsoid by itself, however, does not indicate the plane on which the given traction vector acts. Only for the case where the stress vector lies along one of the principal directions it is possible to know the direction of the plane, as the principal stresses act perpendicular to their planes. To find the orientation of any other plane we used the stress-director surface or stress director quadric represented by the equationThe stress represented by a radius-vector of the stress ellipsoid acts on a plane oriented parallel to the tangent plane to the stress-director surface at the point of its intersection with the radius-vector.".
- Lame's_stress_ellipsoid wikiPageID "27071123".
- Lame's_stress_ellipsoid wikiPageRevisionID "545891960".
- Lame's_stress_ellipsoid hasPhotoCollection Lame's_stress_ellipsoid.
- Lame's_stress_ellipsoid subject Category:Classical_mechanics.
- Lame's_stress_ellipsoid subject Category:Elasticity_(physics).
- Lame's_stress_ellipsoid subject Category:Materials_science.
- Lame's_stress_ellipsoid subject Category:Mechanics.
- Lame's_stress_ellipsoid subject Category:Solid_mechanics.
- Lame's_stress_ellipsoid comment "Lame's stress ellipsoid (Figure coming) is an alternative to Mohr's circle for the graphical representation of the stress state at a point. The surface of the ellipsoid represents the locus of the endpoints of all stress vectors acting on all planes passing through a given point in the continuum body.".
- Lame's_stress_ellipsoid label "Elipsoida naprężeń Lamégo".
- Lame's_stress_ellipsoid label "Lame's stress ellipsoid".
- Lame's_stress_ellipsoid label "مجسم ليم الناقص للإجهاد".
- Lame's_stress_ellipsoid sameAs Elipsoida_naprężeń_Lamégo.
- Lame's_stress_ellipsoid sameAs m.0bs2czl.
- Lame's_stress_ellipsoid sameAs Q6481646.
- Lame's_stress_ellipsoid sameAs Q6481646.
- Lame's_stress_ellipsoid wasDerivedFrom Lame's_stress_ellipsoid?oldid=545891960.
- Lame's_stress_ellipsoid isPrimaryTopicOf Lame's_stress_ellipsoid.