Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads

Simmonds, J. G.
Springer
Published 1990
ISSN:
1573-2681
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Physics
Notes:
Abstract An infinite, horizontal, elastically isotropic plate is subjected to a distributed vertical, axisymmetric load, part of which is a body force and part of which is a surface traction. The resulting 3-dimensional stresses and displacements are found with the aid of Love's stress function and Hankel transforms. From these, the sum of the principal stress couples, the average rotation of radial fibers, and the average vertical deflection are computed and compared against the predictions of classical and Reissner's shear-deformation plate theory. Remarkably, the elasticity and plate theory predictions for the stress couples and the rotation agree if Poisson's ratio is zero. In general, for smoothly varying loads, the predictions of Reissner's theory are closer than those of classical theory to the predictions of elasticity theory. However, if a part of the load is (nearly) concentrated, then it is shown that the singularities in the sum of the principal stress couples and in the rotation predicted by Reissner's theory are too strong (because his theory accounts for normal stress effects based on smoothly varying loads). Moreover, if the concentrated part of the external load is a uniformly distributed line load through the thickness, then classical theory predicts the correct singularity in these variables, although with an erroneous strength. On the other hand, Reissner's theory correctly predicts the logarithmic singularity in the average vertical deflection (for any type of concentrated load), although with an erroneous strength.
Type of Medium:
Electronic Resource
URL:
_version_ 1798296667108147200
autor Simmonds, J. G.
autorsonst Simmonds, J. G.
book_url http://dx.doi.org/10.1007/BF00054804
datenlieferant nat_lic_papers
hauptsatz hsatz_simple
identnr NLM19376704X
issn 1573-2681
journal_name Journal of elasticity
materialart 1
notes Abstract An infinite, horizontal, elastically isotropic plate is subjected to a distributed vertical, axisymmetric load, part of which is a body force and part of which is a surface traction. The resulting 3-dimensional stresses and displacements are found with the aid of Love's stress function and Hankel transforms. From these, the sum of the principal stress couples, the average rotation of radial fibers, and the average vertical deflection are computed and compared against the predictions of classical and Reissner's shear-deformation plate theory. Remarkably, the elasticity and plate theory predictions for the stress couples and the rotation agree if Poisson's ratio is zero. In general, for smoothly varying loads, the predictions of Reissner's theory are closer than those of classical theory to the predictions of elasticity theory. However, if a part of the load is (nearly) concentrated, then it is shown that the singularities in the sum of the principal stress couples and in the rotation predicted by Reissner's theory are too strong (because his theory accounts for normal stress effects based on smoothly varying loads). Moreover, if the concentrated part of the external load is a uniformly distributed line load through the thickness, then classical theory predicts the correct singularity in these variables, although with an erroneous strength. On the other hand, Reissner's theory correctly predicts the logarithmic singularity in the average vertical deflection (for any type of concentrated load), although with an erroneous strength.
package_name Springer
publikationsjahr_anzeige 1990
publikationsjahr_facette 1990
publikationsjahr_intervall 8009:1990-1994
publikationsjahr_sort 1990
publisher Springer
reference 23 (1990), S. 219-232
search_space articles
shingle_author_1 Simmonds, J. G.
shingle_author_2 Simmonds, J. G.
shingle_author_3 Simmonds, J. G.
shingle_author_4 Simmonds, J. G.
shingle_catch_all_1 Simmonds, J. G.
Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
Abstract An infinite, horizontal, elastically isotropic plate is subjected to a distributed vertical, axisymmetric load, part of which is a body force and part of which is a surface traction. The resulting 3-dimensional stresses and displacements are found with the aid of Love's stress function and Hankel transforms. From these, the sum of the principal stress couples, the average rotation of radial fibers, and the average vertical deflection are computed and compared against the predictions of classical and Reissner's shear-deformation plate theory. Remarkably, the elasticity and plate theory predictions for the stress couples and the rotation agree if Poisson's ratio is zero. In general, for smoothly varying loads, the predictions of Reissner's theory are closer than those of classical theory to the predictions of elasticity theory. However, if a part of the load is (nearly) concentrated, then it is shown that the singularities in the sum of the principal stress couples and in the rotation predicted by Reissner's theory are too strong (because his theory accounts for normal stress effects based on smoothly varying loads). Moreover, if the concentrated part of the external load is a uniformly distributed line load through the thickness, then classical theory predicts the correct singularity in these variables, although with an erroneous strength. On the other hand, Reissner's theory correctly predicts the logarithmic singularity in the average vertical deflection (for any type of concentrated load), although with an erroneous strength.
1573-2681
15732681
Springer
shingle_catch_all_2 Simmonds, J. G.
Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
Abstract An infinite, horizontal, elastically isotropic plate is subjected to a distributed vertical, axisymmetric load, part of which is a body force and part of which is a surface traction. The resulting 3-dimensional stresses and displacements are found with the aid of Love's stress function and Hankel transforms. From these, the sum of the principal stress couples, the average rotation of radial fibers, and the average vertical deflection are computed and compared against the predictions of classical and Reissner's shear-deformation plate theory. Remarkably, the elasticity and plate theory predictions for the stress couples and the rotation agree if Poisson's ratio is zero. In general, for smoothly varying loads, the predictions of Reissner's theory are closer than those of classical theory to the predictions of elasticity theory. However, if a part of the load is (nearly) concentrated, then it is shown that the singularities in the sum of the principal stress couples and in the rotation predicted by Reissner's theory are too strong (because his theory accounts for normal stress effects based on smoothly varying loads). Moreover, if the concentrated part of the external load is a uniformly distributed line load through the thickness, then classical theory predicts the correct singularity in these variables, although with an erroneous strength. On the other hand, Reissner's theory correctly predicts the logarithmic singularity in the average vertical deflection (for any type of concentrated load), although with an erroneous strength.
1573-2681
15732681
Springer
shingle_catch_all_3 Simmonds, J. G.
Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
Abstract An infinite, horizontal, elastically isotropic plate is subjected to a distributed vertical, axisymmetric load, part of which is a body force and part of which is a surface traction. The resulting 3-dimensional stresses and displacements are found with the aid of Love's stress function and Hankel transforms. From these, the sum of the principal stress couples, the average rotation of radial fibers, and the average vertical deflection are computed and compared against the predictions of classical and Reissner's shear-deformation plate theory. Remarkably, the elasticity and plate theory predictions for the stress couples and the rotation agree if Poisson's ratio is zero. In general, for smoothly varying loads, the predictions of Reissner's theory are closer than those of classical theory to the predictions of elasticity theory. However, if a part of the load is (nearly) concentrated, then it is shown that the singularities in the sum of the principal stress couples and in the rotation predicted by Reissner's theory are too strong (because his theory accounts for normal stress effects based on smoothly varying loads). Moreover, if the concentrated part of the external load is a uniformly distributed line load through the thickness, then classical theory predicts the correct singularity in these variables, although with an erroneous strength. On the other hand, Reissner's theory correctly predicts the logarithmic singularity in the average vertical deflection (for any type of concentrated load), although with an erroneous strength.
1573-2681
15732681
Springer
shingle_catch_all_4 Simmonds, J. G.
Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
Abstract An infinite, horizontal, elastically isotropic plate is subjected to a distributed vertical, axisymmetric load, part of which is a body force and part of which is a surface traction. The resulting 3-dimensional stresses and displacements are found with the aid of Love's stress function and Hankel transforms. From these, the sum of the principal stress couples, the average rotation of radial fibers, and the average vertical deflection are computed and compared against the predictions of classical and Reissner's shear-deformation plate theory. Remarkably, the elasticity and plate theory predictions for the stress couples and the rotation agree if Poisson's ratio is zero. In general, for smoothly varying loads, the predictions of Reissner's theory are closer than those of classical theory to the predictions of elasticity theory. However, if a part of the load is (nearly) concentrated, then it is shown that the singularities in the sum of the principal stress couples and in the rotation predicted by Reissner's theory are too strong (because his theory accounts for normal stress effects based on smoothly varying loads). Moreover, if the concentrated part of the external load is a uniformly distributed line load through the thickness, then classical theory predicts the correct singularity in these variables, although with an erroneous strength. On the other hand, Reissner's theory correctly predicts the logarithmic singularity in the average vertical deflection (for any type of concentrated load), although with an erroneous strength.
1573-2681
15732681
Springer
shingle_title_1 Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
shingle_title_2 Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
shingle_title_3 Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
shingle_title_4 Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
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timestamp 2024-05-06T09:55:43.947Z
titel Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
titel_suche Pointwise errors in the classical and in Reissner's linear theory of plates, especially for concentrated loads
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