Optimal Forms of Shallow Shells With Circular Boundary, Part 3: Maximum Enclosed Volume

1984 ◽  
Vol 51 (3) ◽  
pp. 536-539 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Spherical Shell ◽  
Surface Area ◽  
Material Surface ◽  
Uniform Thickness ◽  
Base Plane ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Boundary Part ◽  
Uniformly Distributed Loads

In Parts 1 and 2, we determined optimal forms of shallow shells with respect to vibration and stability, respectively. In this final part, we consider a given load and find the shell form for which the volume between the base plane and the deflected shell is a maximum. As before, the shell is assumed to be thin, elastic, and axisymmetric, with a given circular boundary that is either clamped or simply supported. The material, surface area, and uniform thickness of the shell are specified. Both uniformly distributed loads and concentrated central loads are treated. In the numerical results, the maximum enclosed volume is on the order of 10 percent higher than that for the corresponding spherical shell.

Optimal Forms of Shallow Shells With Circular Boundary, Part 1: Maximum Fundamental Frequency

1984 ◽  
Vol 51 (3) ◽  
pp. 526-530 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson ◽  
R. Parbery
Keyword(s):  
Boundary Conditions ◽  
Fundamental Frequency ◽  
Iterative Procedure ◽  
Material Surface ◽  
Uniform Thickness ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Axisymmetric Shell ◽  
Boundary Part

Thin, shallow, elastic shells with given circular boundary are considered. We seek the axisymmetric shell form which maximizes the fundamental frequency of vibration. The boundary conditions, material, surface area, and uniform thickness of the shell are specified. We employ a bimodal formulation and use an iterative procedure based on the optimality condition to obtain optimal forms. Results are presented for clamped and simply supported boundary conditions. For the clamped case, the optimal forms have zero slope at the boundary. The maximum fundamental frequency is significantly higher than that for the corresponding spherical shell if the boundary is clamped, but only slightly higher if it is simply supported.

Optimal Forms of Shallow Shells With Circular Boundary, Part 2: Maximum Buckling Load

1984 ◽  
Vol 51 (3) ◽  
pp. 531-535 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Critical Load ◽  
Elastic Shell ◽  
Material Surface ◽  
Fundamental Vibration ◽  
Uniform Loading ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Boundary Part

In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.

Optimal Forms of Shallow Cylindrical Panels With Respect to Vibration and Stability

1986 ◽  
Vol 53 (1) ◽  
pp. 135-140 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Surface Area ◽  
Fundamental Frequency ◽  
Axial Load ◽  
Cylindrical Panel ◽  
Buckling Load ◽  
Material Surface ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Cylindrical Panels

Thin, shallow, elastic, cylindrical panels with rectangular planform are considered. We seek the midsurface form which maximizes the fundamental frequency of vibration, and the form which maximizes the buckling value of a uniform axial load. The material, surface area, and uniform thickness of the panel are specified. The curved edges are simply supported, while the straight edges are either simply supported or clamped. For the clamped case, the optimal panels have zero slope at the edges. In the examples, the maximum fundamental frequency is up to 12 percent higher than that of the corresponding circular cylindrical panel, while the buckling load is increased by as much as 95 percent. Most of the solutions are bimodal, while the rest are either unimodal or trimodal.

Bending of a simply-supported shallow spherical shell under a uniform line load on a part of a parallel circle

1967 ◽  
Vol 63 (1) ◽  
pp. 239-246 ◽  
Author(s):  
D. N. Mitra
Keyword(s):  
Differential Equation ◽  
Spherical Shell ◽  
Fourth Order ◽  
Bessel Functions ◽  
Order Differential Equation ◽  
Transverse Displacement ◽  
Line Load ◽  
Shallow Shells ◽  
Simply Supported ◽  
Stress Functions

AbstractThe two fourth-order partial differential equations giving the transverse displacement and the stress functions for shallow shells are reduced to a sixth-order differential equation in one variable which has been solved, and the values of displacements, stress resultants and couples are all expressed in terms of Bessel Functions of imaginary argument. Numerical values of the displacement presented for points on the shell on different meridian lines, showed that on the symmetrical line deflexion is maximum at the point of loading but the point of maximum deflexion shifts gradually towards the pole.

Analysis of Interface Deformation of Steel-Concrete-Steel Sandwich Beam

2012 ◽  
Vol 525-526 ◽  
pp. 357-360
Author(s):  
Pei Xiu Xia ◽  
Guang Ping Zou ◽  
Zhong Liang Chang
Keyword(s):  
Sandwich Beam ◽  
Analytical Models ◽  
Sandwich Beams ◽  
Interface Deformation ◽  
Simply Supported ◽  
Interface Slip ◽  
Steel Panels ◽  
Uniformly Distributed Loads ◽  
Relationship Of ◽  
The Relationship

The effect of the interface slip is neglected in most studies on calculating deflection of sandwich beams. By taking a simply supported sandwich beams under uniformly distributed loads as an example, simplified analytical models of the interface slip are established, and corresponding clculation formulas of interface slip between steel panels and concrete and section curvatures are derived. The formula for deflection of sandwich beams are then presented. This formula reflects the relationship of influence each other between the interface slip and deflection.

Computation of natural frequencies of skewed slabs using equivalent rectangular slab concept

1980 ◽  
Vol 7 (2) ◽  
pp. 384-388 ◽  
Author(s):  
T. I. Campbell ◽  
W. H. Siu
Keyword(s):  
Isotropic Material ◽  
Natural Frequencies ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Linear Elastic ◽  
Rectangular Slab

The natural frequencies of skewed slabs (in the shape of a parallelogram) of uniform thickness and linear elastic isotropic material are considered. It is shown that the natural frequencies of a skewed slab can be related to those of the corresponding rectangular slab by means of an equivalent rectangular slab concept. Charts are presented to allow the computation of the natural frequencies of one-, two-, and three-span symmetric skewed slabs, which are simply supported at each end and free along each edge.

scholarly journals Analysis of critical imposed load of plate using variational calculus

2021 ◽  
Vol 4 (1) ◽  
pp. 13-23
Author(s):  
Festus C. Onyeka ◽  
Thompson E. Okeke
Keyword(s):  
Numerical Analysis ◽  
Variational Calculus ◽  
Width Ratio ◽  
Rectangular Plates ◽  
Span Length ◽  
Simply Supported ◽  
The Third ◽  
Load Analysis ◽  
Uniformly Distributed Loads ◽  
Maximum Threshold

This work studied the critical load analysis of rectangular plates, carrying uniformly distributed loads utilizing direct variational energy calculus. The aim of this study is to establish the techniques for calculating the critical lateral imposed loads of the plate before deflection attains the specified maximum threshold, qiw as well as its corresponding critical lateral imposed load before the plate reaches an elastic yield point. The formulated potential energy by the static elastic theory of the plate was minimized to get the shear deformation and coefficient of deflection. The plates under consideration are clamped at the first and second edges, free of support at the third edge and simply supported at the fourth edge (CCFS). From the numerical analysis obtained, it is found that the critical lateral imposed loads (qiw and qip) increase as the thickness (t) of plate increases, and decrease as the length to width ratio increases. This suggests that as the thickness increases, the allowable deflection improves the safety of the plate, whereas an increase in the span (length) of the plate increases the failure tendency of the plate structure.

scholarly journals Statistical Analysis of Anode Efficiency in Electrochemical Treatment of Wastewater and Sludge

2020 ◽  
Vol 7 (4) ◽  
pp. 1041-1064
Author(s):  
Jannatul Rumky ◽  
Walter Z. Tang ◽  
Mika Sillanpää
Keyword(s):  
Regression Analysis ◽  
Surface Area ◽  
Removal Efficiency ◽  
Pollutant Removal ◽  
Coagulation System ◽  
Material Surface ◽  
Electrode Distance ◽  
Reactor Volume ◽  
Electrochemical Processes ◽  
Electro Oxidation

Abstract Electrochemical processes have proven their potential as effective technologies to treat wastewater from industrial, urban and agricultural activities, and thus, contribute towards a cleaner environment. In this study, we aimed to assess the effectiveness of the leading electrochemical technologies, such as electro-oxidation, electrochemical coagulation and electrochemical advanced oxidation processes (EAOPs), statistically for different types of anodes for the removal of various pollutants from wastewater along with their treatment efficiency. Anode is considered as a source of electron and an essential part of electrochemical processes. So, we have evaluated the relationship between different anode features such as anodic material, surface area versus removal of chemical oxygen demand (COD), dissolved organic carbon (DOC) and colour in various wastewater treatment plants (WWTPs) by IBM SPSS Statistics 26. Apart from that, various process characteristics such as inter-electrode distance, system pH, reactor volume, current density and voltage were also considered in this investigation. From the regression analysis of the electrochemical coagulation system, it was found that the removal efficiency of pollutants is enhanced by the surface area of the electrodes along with the inter-electrode distance. Regarding electro-oxidation, it was seen that COD and colour removal are both dependent on the reaction time of the system, while the DOC removal rate of different EAOPs was strongly related to the reactor volume. Furthermore, the uncertainty of the regression analysis on pollutant removal efficiency prediction was assessed. Finally, sensitivity analysis was done by Monte-Carlo method to check modest changes from input variables.

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