Numerical analysis of variable thickness plates

1966 ◽  
Vol 1 (3) ◽  
pp. 231-238 ◽  
Author(s):  
C. T. Harnden ◽  
K. R. Rushton
Keyword(s):  
Numerical Analysis ◽  
Difference Equation ◽  
Variable Thickness ◽  
Analogue Computer ◽  
Finite Difference Equation ◽  
Step Method ◽  
Electrical Analogue ◽  
Simply Supported ◽  
Laterally Loaded ◽  
Clamped Edges

Exact solutions of the full finite difference equation to the deflection of laterally loaded variable thickness plates are obtained by a step-by-step numerical method. A pure-resistance electrical analogue computer is used to perform the calculations. Certain mixed derivative terms which cannot be included conveniently in the analogue equations are represented as a modification to the load. The resultant step-by-step method converges rapidly to give results which differ from analytical values by less than 0.5 per cent. Plates with both simply supported and clamped edges are considered.

scholarly journals Evaluation of p-y Curves and p-multiplier of Pile Groups Corresponding to Sand Properties Change Based on 3D Numerical Analysis

2020 ◽  
Vol 20 (4) ◽  
pp. 207-217
Author(s):  
Yongjin Choi ◽  
Jaehun Ahn
Keyword(s):  
Numerical Analysis ◽  
Soil Properties ◽  
Pile Group ◽  
Friction Angle ◽  
Dominant Factor ◽  
Group Effect ◽  
Pile Groups ◽  
Dense Sand ◽  
Laterally Loaded Pile ◽  
Laterally Loaded

The <i>p-y</i> curve method and </i>p</i>-multiplier (<i>P<sub>m</sub></i>), which implies a group effect, are widely used to analyze the nonlinear behaviors of laterally loaded pile groups. Factors affecting <i>P<sub>m</sub></i> includes soil properties as well as group pile geometry and configuration. However, research on the change in <i>P<sub>m</sub></i> corresponding to soil properties has not been conducted well. In this study, in order to evaluate the effect of soil properties on the group effect in a laterally-loaded pile group installed in sandy soil, numerical analysis for a single pile and 3×3 pile group installed in loose, medium, and dense sand, was performed using the 3D numerical analysis program, Plaxis 3D. Among the factors considered in this study, the column location of the pile was the most dominant factor for <i>P<sub>m</sub></i>. The effect of the sand property change on <i>P<sub>m</sub></i> was not as significant as that of the column location of the pile. However, as the sand became denser and the friction angle increased, the group effect increased, leading to a decrease in <i>P<sub>m</sub></i> of approximately 0.1. This trend was similar to the result reported in a previous laboratory-scale experimental study.

scholarly journals Polya Counting Theory Applied to Combination of Edge Conditions for Generally Shaped Isotropic Plates

2019 ◽  
Vol 2 (2) ◽  
pp. 194-202
Author(s):  
Yoshihiro Narita
Keyword(s):  
Material Properties ◽  
Structural Design ◽  
Plate Boundary ◽  
Trial And Error ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Edge Conditions ◽  
Structural Responses ◽  
Structural Behaviors ◽  
Clamped Edges

Structural behaviors of plate components, such as internal stress, deflection, buckling and dynamic response, are important in the structural design of aerospace, mechanical, civil and other industries. These behaviors are known to be affected not only by plate shapes and material properties but also by edge conditions. Any one of the three classical edge conditions in bending, namely free, simply supported and clamped edges, may be used to model the constraint along an edge of plates. Along the entre boundary with plural edges, there exist a wide variety of combinations in the entire plate boundary, each giving different values of structural responses. For counting the total number of possible combinations, the present paper considers Polya counting theory in combinatorial mathematics. For various plate shapes, formulas are derived for counting exact numbers in combination. In some examples, such combinations are confirmed in the figures by a trial and error approach.

A Levy-Type Solution for a Rectangular Plate of Variable Thickness

1958 ◽  
Vol 25 (2) ◽  
pp. 297-298
Author(s):  
H. D. Conway
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Variable Thickness ◽  
Thickness Variation ◽  
Type Solution ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions ◽  
Plate Of Variable Thickness

Abstract A solution is given for the bending of a uniformly loaded rectangular plate, simply supported on two opposite edges and having arbitrary boundary conditions on the others. The thickness variation is taken as exponential in order to make the solution tractable, and thus closely approximates to uniform taper if the latter is small.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

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