A DYNAMIC MODEL FOR THICK ELASTIC PLATES

1999 ◽  
Vol 221 (2) ◽  
pp. 187-203 ◽  
Author(s):  
Zeng Deshun ◽  
W. Hauger ◽  
M. Matthes ◽  
S. Schreiber
Keyword(s):  
Dynamic Model ◽  
Elastic Plates ◽  
Thick Elastic Plates

Thermal Stresses in Moderately Thick Elastic Plates

1959 ◽  
Vol 26 (3) ◽  
pp. 432-436
Author(s):  
B. E. Gatewood
Keyword(s):  
Temperature Gradient ◽  
Plane Stress ◽  
Thermal Stresses ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Elastic Plates ◽  
Plate Length ◽  
Moderately Thick Plates ◽  
Thick Elastic Plates ◽  
Thickness Variable

Abstract The three-dimensional stresses in the plate are investigated without using the plane-stress or plane-strain assumptions, the thickness of the plate being limited so that the normal stress in the thickness direction can be taken as a polynomial in the thickness variable. The temperature is taken as a polynomial in the thickness variable but with relatively large, though restricted, gradients with respect to the co-ordinates of the plane of the plate. For the case of the temperature constant in thickness variable, the stresses in the plane of the plate are presented as the plane-stress solution plus correcting terms due to the plate thickness, where the correcting terms involve the product of the temperature gradient and the ratio of the plate thickness to the plate length in the direction of the temperature gradient. In many cases the corrections are small even for moderately thick plates.

ON THREE-DIMENSIONAL INITIAL-BOUNDARY PROBLEMS OF THICK ELASTIC PLATES’ DYNAMICS

2021 ◽  
Vol 3 ◽  
pp. 34-49
Author(s):  
Vladimir Stoyan ◽  
◽  
Sergey Voloshchuk ◽  
Keyword(s):  
Root Mean Square ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Initial Boundary ◽  
Accuracy Evaluation ◽  
Mean Square ◽  
Elastic Plates ◽  
Boundary Problems ◽  
Computational Mathematics ◽  
Thick Elastic Plates

Complex problems of three-dimensional elasticity theory for thick elastic plates with arbitrary geometry of their lateral surface are solved. Analytical dependencies of the components of the elastic dynamic displacements’ field of the plate’s inner points from the boundary-surface external-dynamic disturbing factors, defined by continuous functions or their values’ vectors, are constructed. It is assumed, that these disturbances have a classically defined powerful character, or are specified by a certain number of differential transformations of the field’s components of the plate’s dynamic displacement points. The absence of quantitative and qualitative restrictions on the determined transformations of the initial-boundary problems of the considered plates’ dynamics makes it incorrect and unsolvable by methods of classical and computational mathematics. The methodology of root-mean square mathematical modeling of discretely and continuously specified observations for the initial-boundary plate’s condition by the system of modeling functions and their values’ vectors is proposed in the paper. Constructed in this way field’s components of spatial-dynamic displacements of the plate’s points, precisely satisfying classical Lyame equation, with the available information on its initial-boundary condition, are agreed according to the root-mean square criterion. The problem of the obtained solutions’ ambiguity is investigated, their accuracy evaluation in accordance with the information on the external- dynamic condition of the investigated plate is conducted. The plate’s dynamics in the particular mode, for cases of information lack on external- dynamic influences on it and under the conditions of its geometric background according to spatial coordinates. The computer realization of the obtained mathematical results is engineeringly simple and can be easily implemented with the help of well-known methods of computational mathematics.

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