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.

Bending of Elastically Restrained Rectangular Plates Under Uniform Pressure

1958 ◽  
Vol 62 (575) ◽  
pp. 834-836 ◽  
Author(s):  
C. Lakshmi Kantham
Keyword(s):  
Natural Frequencies ◽  
Unit Length ◽  
Rectangular Plates ◽  
Uniform Pressure ◽  
Simply Supported ◽  
Edge Conditions ◽  
Definition Of ◽  
Elastically Restrained ◽  
Clamped Edges ◽  
Clamped Edge

In the bending and vibration of plates it is found that the values of maximum deflection and natural frequencies, respectively, vary considerably from the simply-supported to clamped edge conditions. For an estimation of these characteristics in the intermediate range a generalised boundary condition may be assumed, of which the simply-supported and clamped edges become limiting cases. While Bassali considers the ratio of edge moment to the cross-wise moment as a constant, Newmark, Lurie and Klein and other investigators, in their analyses of various structures, consider that moment and slope at an end are proportional.Here the definition of elastic restraint as given by Timoshenko, α=βM, is followed, where α is the slope at any edge, M the corresponding edge moment per unit length while β is the elastic restraint factor. β→0 and β→∞ represent the two limiting cases of simply-supported and clamped edge conditions.

scholarly journals Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

2021 ◽  
pp. 1-11
Author(s):  
Param D. Gajbhiye ◽  
Vishisht Bhaiya ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Shear Mode ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Thickness Shear

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.

Combinations for the Free Vibration Behaviors of Anisotropic Rectangular Plates Under General Edge Conditions

1999 ◽  
Author(s):  
Yoshihiro Narita
Keyword(s):  
Free Vibration ◽  
Structural Design ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Technical Information ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Plate Models ◽  
Edge Conditions ◽  
Anisotropic Rectangular Plates

Abstract The free vibration behavior of rectangular plates provides important technical information in structural design, and the natural frequencies are primarily affected by the boundary conditions as well as aspect and thickness ratios. One of the three classical edge conditions, i.e., free, simple supported and clamped edges, may be used to model the constraint along an edge of the rectangle. Along the entire boundary with four edges, there exist a wide variety of combinations in the edge conditions, each yielding different natural frequencies and mode shapes. For counting the total number of possible combinations, the present paper introduces the Polya counting theory in combinatorial mathematics, and formulas are derived for counting the exact numbers. A modified Ritz method is then developed to calculate natural frequencies of anisotropic rectangular plates under any combination of the three edge conditions and is used to numerically verify the numbers. In numerical experiments, the number of combinations in the free vibration behaviors is determined for some plate models by using the derived formulas, and are corroborated by counting the numbers of different sets of the natural frequencies that are obtained from the Ritz method.

Efficient Structural Design Using a Numerical Optimization Technique

2019 ◽  
Author(s):  
Qian Wang ◽  
Lucas Schmotzer ◽  
Yongwook Kim
Keyword(s):  
Structural Design ◽  
Numerical Optimization ◽  
Optimization Technique ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Convergence Criteria ◽  
Efficient Design ◽  
Concrete Building ◽  
Gradient Based ◽  
Structural Responses

<p>Structural designs of complex buildings and infrastructures have long been based on engineering experience and a trial-and-error approach. The structural performance is checked each time when a design is determined. An alternative strategy based on numerical optimization techniques can provide engineers an effective and efficient design approach. To achieve an optimal design, a finite element (FE) program is employed to calculate structural responses including forces and deformations. A gradient-based or gradient-free optimization method can be integrated with the FE program to guide the design iterations, until certain convergence criteria are met. Due to the iterative nature of the numerical optimization, a user programming is required to repeatedly access and modify input data and to collect output data of the FE program. In this study, an approximation method was developed so that the structural responses could be expressed as approximate functions, and that the accuracy of the functions could be adaptively improved. In the method, the FE program was not required to be directly looped in the optimization iterations. As a practical illustrative example, a 3D reinforced concrete building structure was optimized. The proposed method worked very well and optimal designs were found to reduce the torsional responses of the building.</p>

Eigenfrequencies of Continuous Plates With Arbitrary Number of Equal Spans

1979 ◽  
Vol 46 (3) ◽  
pp. 656-662 ◽  
Author(s):  
Isaac Elishakoff ◽  
Alexander Sternberg
Keyword(s):  
Arbitrary Number ◽  
Wave Number ◽  
Analytical Technique ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Simple Support ◽  
Transcendental Equations ◽  
Rigid Supports ◽  
Numerical Complexity

An approximate analytical technique is developed for determination of the eigenfrequencies of rectangular isotropic plates continuous over rigid supports at regular intervals with arbitrary number of spans. All possible combinations of simple support and clamping at the edges are considered. The solution is given by the modified Bolotin method, which involves solution of two problems of the Voigt-Le´vy type in conjunction with a postulated eigenfrequency/wave-number relationship. These auxiliary problems yield a pair of transcendental equations in the unknown wave numbers. The number of spans figures explicitly in one of the transcendental equations, so that numerical complexity does not increase with the number of spans. It is shown that the number of eigenfrequencies associated with a given pair of mode numbers equals that of spans. The essential advantage of the proposed method is the possibility of finding the eigenfrequencies for any prescribed pair of mode numbers. Moreover, for plates simply supported at two opposite edges and continuous over rigid supports perpendicular to those edges, the result is identical with the exact solution.

Numerical Investigation on Weld-Induced Imperfections in Aluminum Ship Plates

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Bai-Qiao Chen ◽  
C. Guedes Soares
Keyword(s):  
Finite Element ◽  
Aluminum Alloy ◽  
Material Properties ◽  
Welding Process ◽  
Finite Element Models ◽  
Finite Element Analyses ◽  
Temperature Dependent ◽  
Military Applications ◽  
Structural Responses ◽  
Or In Military

The present work aims at better understanding and predicting the thermal and structural responses of aluminum components subjected to welding, contributing to the design and fabrication of aluminum ships such as catamarans, lifesaving boats, tourist ships, and fast ships used in transportation or in military applications. Taken into consideration the moving heat source in metal inert gas (MIG) welding, finite element models of plates made of aluminum alloy are established and validated against published experimental results. Considering the temperature-dependent thermal and mechanical properties of the aluminum alloy, thermo-elasto-plastic finite element analyses are performed to determine the size of the heat-affected zone (HAZ), the temperature histories, the distortions, and the distributions of residual stresses induced by the welding process. The effects of the material properties on the finite element analyses are discussed, and a simplified model is proposed to represent the material properties based on their values at room temperature.

The Plastic Buckling of Axially Compressed Square Tubes

1992 ◽  
Vol 59 (2) ◽  
pp. 276-282 ◽  
Author(s):  
S. Li ◽  
S. R. Reid
Keyword(s):  
Deformation Theory ◽  
Buckling Analysis ◽  
Rectangular Plates ◽  
Plastic Buckling ◽  
Buckling Mode ◽  
Important Conclusion ◽  
Simply Supported ◽  
Edge Conditions ◽  
Crushing Behavior ◽  
Incremental Theory Of Plasticity

A plastic buckling analysis for axially compressed square tubes is described in this paper. Deformation theory is used together with the realistic edge conditions for the panels of the tube introduced in our previous paper (Li and Reid, 1990), referred to hereafter as LR. The results obtained further our understanding of a number of problems related to the plastic buckling of axially compressed square tubes and simply supported rectangular plates, which have remained unsolved hitherto and seem rather puzzling. One of these is the discrepancy between experimental results and the results of plastic buckling analysis performed using the incremental theory of plasticity and the unexpected agreement between the results of calculations based on deformation theory for plates and experimental data obtained from tests conducted on tubes. The non-negligible difference between plates and tubes obtained in the present paper suggests that new experiments should be carried out to provide a more accurate assessment of the predictions of the two theories. Discussion of the results herein also advances our understanding of the compact crushing behavior of square tubes beyond that given in LR. An important conclusion reached is that strain hardening cannot be neglected for the plastic buckling analysis of square tubes even if the degree of hardening is small since doing so leads to an unrealistic buckling mode.

Aspects of a Safety Operation of Service Robots on Glass Walls

2015 ◽  
Vol 772 ◽  
pp. 461-465
Author(s):  
Marcel Horák ◽  
František Novotný ◽  
Michal Starý ◽  
Josef Černohorský
Keyword(s):  
Material Properties ◽  
Service Robots ◽  
Vacuum System ◽  
Robot Motion ◽  
High Rise ◽  
State Of Stress ◽  
Service Operation ◽  
Edge Conditions ◽  
Real Composition ◽  
Safety Operation

The paper focuses on problems of the safety operation of service robots on glass facades of high-rise buildings exposed to a local additional load during the robot motion and any subsequent service operation (e.g. cleaning, diagnostics, mounting). Owing to afraid of a possible glass cracking and a subsequent destruction, the authors pay attention to an analysis of the strength of façade glass sheets being in contact with the robot holding-down vacuum system as well as with the supporting steel construction. With a view of appraising a state of stress, a computer model was build up respecting the real composition of façade glass, material properties and contact edge conditions. The paper presents achieved results by means of graphic outputs, and in conclusion, it discusses them with aim to supply owners of service robots from a sphere of the building administration a number of details.

scholarly journals Structural Design for a 10-GWh SMES Vacuum Vessel

1978 ◽  
Vol 100 (3) ◽  
pp. 263-270
Author(s):  
J. G. Bennett ◽  
C. A. Anderson
Keyword(s):  
Cylindrical Shell ◽  
Approximate Solution ◽  
Elastic Deformation ◽  
Material Properties ◽  
Structural Design ◽  
Shell Thickness ◽  
Construction Cost ◽  
Vacuum Vessel ◽  
Nonlinear Elastic

An approximate solution to the problem of the nonlinear elastic deformation of a periodically point-supported cylindrical shell is obtained. This solution is used to investigate the structural design of the vacuum vesssel for the large underground SMES concept. Vacuum vessel designs are evaluated by varying such parameters as shell thickness, support, spacing, material properties and physical configuration to keep the amount of material used and construction cost to a minimum.

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