Constructal design applied to geometrical evaluation of rectangular plates with inclined stiffeners subjected to uniform transverse load

2019 ◽  
Author(s):  
Vinícius Torres Pinto ◽  
◽  
Marcelo Langhinrichs Cunha ◽  
Grégori da Silva Troina ◽  
Kauê Louro Martins ◽  
...  
Keyword(s):  
Transverse Load ◽  
Rectangular Plates ◽  
Constructal Design

scholarly journals Computational Modeling and Constructal Design Theory Applied to the Geometric Optimization of Thin Steel Plates with Stiffeners Subjected to Uniform Transverse Load

Metals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 220 ◽  
Author(s):  
Grégori Troina ◽  
Marcelo Cunha ◽  
Vinícius Pinto ◽  
Luiz Rocha ◽  
Elizaldo dos Santos ◽  
...  
Keyword(s):  
Computational Modeling ◽  
Design Theory ◽  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Geometric Optimization ◽  
Steel Plates ◽  
Transverse Load ◽  
Constructal Design ◽  
Thin Steel ◽  
Reference Plate

Stiffened thin steel plates are structures widely employed in aeronautical, civil, naval, and offshore engineering. Considering a practical application where a transverse uniform load acts on a simply supported stiffened steel plate, an approach associating computational modeling, Constructal Design method, and Exhaustive Search technique was employed aiming to minimize the central deflections of these plates. To do so, a non-stiffened plate was adopted as reference from which all studied stiffened plate’s geometries were originated by the transformation of a certain amount of steel of its thickness into longitudinal and transverse stiffeners. Different values for the stiffeners volume fraction (φ) were analyzed, representing the ratio between the volume of the stiffeners’ material and the total volume of the reference plate. Besides, the number of longitudinal (Nls) and transverse (Nts) stiffeners and the aspect ratio of stiffeners shape (hs/ts, being hs and ts, respectively, the height and thickness of stiffeners) were considered as degrees of freedom. The optimized plates were determined for all studied φ values and showed a deflection reduction of over 90% in comparison with the reference plate. Lastly, the influence of the φ parameter regarding the optimized plates was evaluated defining a configuration with the best structural performance among all analyzed cases.

Geometric evaluation of steel plates subjected to uniform transverse load with rectangular or trapezoidal stiffeners by means constructal design method

2020 ◽  
Vol 3 (2) ◽  
pp. 190
Author(s):  
Vinícius Torres Pinto ◽  
Marcelo Langhinrichs Cunha ◽  
Kauê Louro Martins ◽  
Luiz Alberto Oliveira Rocha ◽  
Mauro De Vasconcellos Real ◽  
...  
Keyword(s):  
Design Method ◽  
Steel Plates ◽  
Transverse Load ◽  
Constructal Design

Large Deflection of Unsymmetric Cross-Ply and Angle-Ply Plates

1976 ◽  
Vol 18 (4) ◽  
pp. 179-183 ◽  
Author(s):  
C. Y. Chia ◽  
M. K. Prabhakara
Keyword(s):  
Boundary Conditions ◽  
Large Deflection ◽  
Perturbation Technique ◽  
Transverse Load ◽  
Load Force ◽  
Rectangular Plates ◽  
Linear Partial Differential Equations ◽  
Transverse Deflection ◽  
Anisotropic Rectangular Plates ◽  
Good Agreement

An approximate solution to the von Karman-type large-deflection equations of unsymmetrically laminated, anisotropic, rectangular plates under uniform transverse load is formulated by the perturbation technique. The membrane boundary conditions are the zero normal and shear boundary forces. By expressing the load, force function and transverse deflection in the form of series, the governing equations and boundary conditions are reduced to a series of linear partial differential equations and boundary conditions. In each approximation a solution is assumed in the form of polynomials which satisfy the associated boundary conditions and physical requirements for deflection and and three membrane forces in unsymmetric cross-ply and angle-ply plates. Taking the first three terms in the truncated series, numerical results are graphically presented for the load-deflection relations, bending moments and membrane forces in unsymmetric cross-ply and angle-ply plates with various values of aspect ratio and total number of layers. The present third approximation is in good agreement with the existing solutions for large deflections of isotropic and unsymmetric angle-ply plates having the ratio of central deflection to thickness up to the value of 2.

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

2021 ◽  
Vol 6 (7) ◽  
pp. 144-152
Author(s):  
Onodagu P. Dinwoke ◽  
Aginam C. Henry ◽  
Uzodinma C. Franklin
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Transverse Load ◽  
Rectangular Plates ◽  
External Work ◽  
Deformation Function ◽  
Depth Ratio ◽  
Out Of Plane

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of  and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

Solution of Some Problems in Bending of Thin Clamped Plates by Means of the Method of Muskhelishvili

1957 ◽  
Vol 24 (2) ◽  
pp. 295-298
Author(s):  
L. I. Deverall
Keyword(s):  
Conformal Mapping ◽  
Mapping Function ◽  
Elliptic Functions ◽  
Transverse Load ◽  
Rectangular Plates ◽  
Convergence Properties ◽  
Clamped Plate ◽  
Central Maximum ◽  
Method Of Solution ◽  
Square Plate

Abstract In this paper, the complex variable method of N. I. Muskhelishvili is applied to the problem of bending for small deflections of a thin, isotropic, homogeneous, clamped plate with transverse load. The functional equation involved in Muskhelishvili’s method is solved by means of series expansions. The necessary conformal mapping functions are found from the Schwarz-Christoffel formula or expansion of elliptic functions. For uniformly loaded square and rectangular plates, the central (maximum) deflection obtained by the method of Muskhelishvili is compared to the corresponding deflections obtained by other methods. Deflections for the square plate are given for three and five terms, respectively, of the series expansion of the conformal mapping function in order to estimate convergence properties of the method of solution. The solution for a uniformly loaded clamped plate of equilateral triangular planform is also discussed. Central deflection for this case is given.

Geometric evaluation of steel plates subjected to uniform transverse load with rectangular or trapezoidal stiffeners by means Constructal Design method

2020 ◽  
Vol 3 (2) ◽  
pp. 1
Author(s):  
Luiz Alberto Oliveira Rocha ◽  
Mauro De Vasconcellos Real ◽  
Elizaldo Domingues Dos Santos ◽  
Liércio André Isoldi ◽  
Kauê Louro Martins ◽  
...  
Keyword(s):  
Design Method ◽  
Steel Plates ◽  
Transverse Load ◽  
Constructal Design

A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates

1992 ◽  
Vol 59 (2S) ◽  
pp. S166-S175 ◽  
Author(s):  
M. Savoia ◽  
J. N. Reddy
Keyword(s):  
Composite Laminates ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Composite Plates ◽  
Approximate Solutions ◽  
Transverse Load ◽  
Rectangular Plates ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity

The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and displacements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and twodimensional theories.

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