Stress and deformation in moderately anisotropic inhomogeneous elastic plates

1995 ◽  
pp. 225-244 ◽  
Author(s):  
A. J. M. Spencer ◽  
P. Watson ◽  
T. G. Rogers
Keyword(s):  
Elastic Plates ◽  
Stress And Deformation

Vibration of an Elastic Circular Plate on an Elastic Half Space—A Direct Approach

1981 ◽  
Vol 48 (1) ◽  
pp. 161-168 ◽  
Author(s):  
S. Krenk ◽  
H. Schmidt
Keyword(s):  
Half Space ◽  
Direct Method ◽  
Power Input ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Solution Technique ◽  
Elastic Plates ◽  
Elastic Circular Plate ◽  
Stress And Deformation ◽  
Phase Angles

The axisymmetric problem of a vibrating elastic plate on an elastic half space is solved by a direct method, in which the contact stresses and the normal displacements of the plate are taken as the unknown functions. First, the influence functions that give the displacements in terms of the stresses are determined for the half space and the plate. Displacement continuity then takes the form of an integral equation. Due to the half space the kernel is weakly singular, and a special solution technique that accounts for this is employed. The solution implies a direct matrix relation between the expansion coefficients of the contact stresses and plate deformations. The solution technique is valid for all frequencies and avoids asympototic expansion in terms of the frequency. The plate is represented by the theory of Reissner and Mindlin, which imposes physical limitations for high frequencies, but the method is easily extended to more general plate theories as well as nonsymmetric oscillations. The results include displacement and phase curves for rigid disks, power input for elastic plates, and typical stress and deformation distributions at selected phase angles. The results show considerable influence from the elastic properties of the plate.

Solving Problems of Vibrational Processes of Isotropically Homogeneous Elastic Plates

2020 ◽  
Vol 41 (9) ◽  
pp. 1846-1853
Author(s):  
N. K. Medeubaev ◽  
A. Zh. Seytmuratov ◽  
M. I. Ramazanov
Keyword(s):  
Elastic Plates

Stress and Deformation

1996 ◽  
Author(s):  
Gerhard Oertel
Keyword(s):  
Differential Equations ◽  
Mathematical Description ◽  
Finite Strain ◽  
Stress Strain ◽  
Complex Problems ◽  
Vector Algebra ◽  
Stress And Deformation

Students of geology who may have only a modest background in mathematics need to become familiar with the theories of stress, strain, and other tensor quantities, so that they can follow, and apply to their own research, developments in modern, quantitative geology. This book, based on a course taught by the author at UCLA, can provide the proper introduction. Included throughout the eight chapters are 136 complex problems, advancing from vector algebra in standard and subscript notations, to the mathematical description of finite strain and its compounding and decomposition. Fully worked solutions to the problems make up the largest part of the book. With their help, students can monitor their progress, and geologists will be able to utilize subscript and matrix notations and formulate and solve tensor problems on their own. The book can be successfully used by anyone with some training in calculus and the rudiments of differential equations.

scholarly journals Stress and deformation analysis of gob-side pre-backfill driving procedure of longwall mining: a case study

2021 ◽  
Author(s):  
Rui Wu ◽  
Penghui Zhang ◽  
Pinnaduwa H. S. W. Kulatilake ◽  
Hao Luo ◽  
Qingyuan He
Keyword(s):  
Rock Mass ◽  
Stress Distribution ◽  
Coal Seam ◽  
Abutment Pressure ◽  
Longwall Mining ◽  
Vertical Stress ◽  
Floor Level ◽  
Working Face ◽  
Floor Heave ◽  
Stress And Deformation

AbstractAt present, non-pillar entry protection in longwall mining is mainly achieved through either the gob-side entry retaining (GER) procedure or the gob-side entry driving (GED) procedure. The GER procedure leads to difficulties in maintaining the roadway in mining both the previous and current panels. A narrow coal pillar about 5–7 m must be left in the GED procedure; therefore, it causes permanent loss of some coal. The gob-side pre-backfill driving (GPD) procedure effectively removes the wasting of coal resources that exists in the GED procedure and finds an alternative way to handle the roadway maintenance problem that exists in the GER procedure. The FLAC3D software was used to numerically investigate the stress and deformation distributions and failure of the rock mass surrounding the previous and current panel roadways during each stage of the GPD procedure which requires "twice excavation and mining". The results show that the stress distribution is slightly asymmetric around the previous panel roadway after the “primary excavation”. The stronger and stiffer backfill compared to the coal turned out to be the main bearing body of the previous panel roadway during the "primary mining". The highest vertical stresses of 32.6 and 23.1 MPa, compared to the in-situ stress of 10.5 MPa, appeared in the backfill wall and coal seam, respectively. After the "primary mining", the peak vertical stress under the coal seam at the floor level was slightly higher (18.1 MPa) than that under the backfill (17.8 MPa). After the "secondary excavation", the peak vertical stress under the coal seam at the floor level was slightly lower (18.7 MPa) than that under the backfill (19.8 MPa); the maximum floor heave and maximum roof sag of the current panel roadway were 252.9 and 322.1 mm, respectively. During the "secondary mining", the stress distribution in the rock mass surrounding the current panel roadway was mainly affected by the superposition of the front abutment pressure from the current panel and the side abutment pressure from the previous panel. The floor heave of the current panel roadway reached a maximum of 321.8 mm at 5 m ahead of the working face; the roof sag increased to 828.4 mm at the working face. The peak abutment pressure appeared alternately in the backfill and the coal seam during the whole procedure of "twice excavation and mining" of the GPD procedure. The backfill provided strong bearing capacity during all stages of the GPD procedure and exhibited reliable support for the roadway. The results provide scientific insight for engineering practice of the GPD procedure.

scholarly journals Effect of peak stress and deformation history on the dynamic tensile behavior of a dual phase steel

2020 ◽  
Author(s):  
J.P. Escobedo ◽  
A.A.H. Ameri ◽  
M. Gonzales ◽  
R. Miller ◽  
H. Wang ◽  
...  
Keyword(s):  
Dual Phase Steel ◽  
Peak Stress ◽  
Tensile Behavior ◽  
Dual Phase ◽  
Deformation History ◽  
Stress And Deformation

Propagation of surface waves past asymmetric elastic plates

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Souvik Kundu ◽  
R. Gayen ◽  
Sourav Gupta
Keyword(s):  
Surface Waves ◽  
Elastic Plates

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals Self-dual singularity through lasing and antilasing in thin elastic plates

2021 ◽  
Vol 103 (13) ◽  
Author(s):  
M. Farhat ◽  
P.-Y. Chen ◽  
S. Guenneau ◽  
Y. Wu
Keyword(s):  
Elastic Plates ◽  
Thin Elastic Plates
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