scholarly journals Constructal design applied to the elastic buckling of thin plates with holes

2013 ◽  
Vol 3 (3) ◽  
Author(s):  
Luiz Rocha ◽  
Liércio Isoldi ◽  
Mauro Vasconcellos Real ◽  
Elizaldo Santos ◽  
Anderson Correia ◽  
...  
Keyword(s):  
Thin Plates ◽  
Elastic Buckling ◽  
Rectangular Hole ◽  
The Finite Element Method ◽  
Perforated Plates ◽  
Simply Supported ◽  
Constructal Design ◽  
Plate Elements ◽  
Optimum Geometry ◽  
Diamond Hole

AbstractElastic buckling is an instability phenomenon that can occur if a slender and thin plate is subjected to axial compression. An important characteristic of the buckling is that the instability may occur at a stress level that is substantially lower than the material yield strength. Besides, the presence of holes in structural plate elements is common. However these perforations cause a redistribution in plate membrane stresses, significantly altering their stability. In this paper the Bejan’s Constructal Design was employed to optimize the geometry of simply supported, rectangular, thin perforated plates subjected to the elastic buckling. Three different centered hole shapes were considered: elliptical, rectangular and diamond. The objective function was to maximize the critical buckling load. The degree of freedom H/L (ratio between width and length of the plate) was kept constant, while H0/L0 (ratio between the characteristic dimensions of the holes) was optimized for several hole volume fractions (ϕ). A numerical model employing the Lanczos method and based on the finite element method was used. The results showed that, for lower values of ϕ the optimum geometry is the diamond hole. For intermediate and higher values of ϕ, the elliptical and rectangular hole, respectively, led to the best performance.

scholarly journals NUMERICAL SIMULATION ANDCONSTRUCTAL DESIGN APPLIED TO THE STUDY OF ELASTIC BUCKLING IN THIN STEEL PLATES WITH OBLONG PERFORATIONS

2018 ◽  
Vol 8 (20) ◽  
Author(s):  
Emilio Gabriel Gonçalves Folzke ◽  
Thiago Da Silveira ◽  
João Paulo Silva Lima ◽  
Luiz Alberto Oliveira Rocha ◽  
Elizaldo Domingues Dos Santos ◽  
...  
Keyword(s):  
Critical Load ◽  
Volume Fraction ◽  
Design Method ◽  
Steel Plates ◽  
Constructal Theory ◽  
Elastic Buckling ◽  
The Finite Element Method ◽  
Perforated Plates ◽  
Constructal Design ◽  
Thin Steel

ABSTRACTBuckling is an instability phenomenon that can happen when a slender plate is subjected to axial compression loads. In addition, perforated plates are often necessary in the engineering field. Throughout this article, the Constructal Design Method, which is based on the Constructal Theory, has been used to evaluate the influence of the hole on thin steel plates under elastic buckling. For that, the different types of holes analyzed were both transversal and longitudinal oblong. They were all placed in the center of the plate. The geometry of the hole varied according to the degree of freedom H0/L0, which relates the dimensions of each type of different hole. The size of the perforation are varied by means the hole volume fraction (f) parameter, that represents the relation between the volume of the hole and the total volume of the plate (without hole). The main goal is to achieve the greatest critical load for the perforated plates. To do so, the ANSYS software, based on the Finite Element Method (FEM), has been used to numerically analyze the elastic buckling in each case. It has been observed the importance of the geometry when seeking superior performances: through a simple fluctuation of the geometry of the hole, once the volume fraction was kept constant, it was possible to achieve a significant increase on the critical loads. Key words: Buckling; Computational Modeling; Critical Load; Constructal Design.

The Effect of Opening on Elastic Buckling of Plates Subjected to Unidirectional Compression Load

2014 ◽  
Vol 574 ◽  
pp. 127-132
Author(s):  
Ting Ting Wang ◽  
Lian Chun Long
Keyword(s):  
Bearing Capacity ◽  
Elastic Buckling ◽  
The Finite Element Method ◽  
Perforated Plates ◽  
Compression Load ◽  
Geometric Factors ◽  
Hole Position ◽  
Buckling Coefficient ◽  
Relationship Of ◽  
The Relationship

This paper has investigated the effect of hole shape, hole size and hole position on elastic buckling of square perforated plates by using the finite element method. According to the effect law of these three geometric factors on buckling bearing capacity, buckling coefficient was obtained by data fitting. The results show that: The plate with circular perforation has the greatest buckling bearing capacity of the three perforation shape plate; When the center perforations have the same area, the relationship between buckling coefficient and perforation size is exponential for the plate with circular hole or square hole, the relationship between buckling coefficient and perforation size is biquadratic for the plate with triangular hole and the greater the perforation size is, the less the buckling bearing capacity will be; For the plate with uniform circular perforation size, The relationship of buckling coefficient and the spacing between perforation center and structure center is quadratic and the greater the spacing is, the less the buckling bearing capacity will be. The results in this paper provide reference for perforation design of plate.

scholarly journals Vibration and Buckling of Square Plates Containing Central Holes

1997 ◽  
Author(s):  
A. B. Sabir ◽  
G. T. Davies
Keyword(s):  
Natural Frequencies ◽  
Elastic Buckling ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Simply Supported ◽  
Mass Matrices ◽  
Out Of Plane ◽  
Circular Holes ◽  
Circular Frequency ◽  
Rigid Body Modes

The finite element method is used to determine the natural frequencies of flat square plates containing centrally located circular or square holes. The plates are subjected to either inplane uniaxial, biaxial or uniformly distributed shear along the four outer edges. These edges are either simply supported or clamped. To determine the stiffness and mass matrices, non conforming rectangular and triangular displacement elements are used to model the out of plane behaviour of the plate. The inplane stress distribution within the plates, which are required in the analysis are determined by using inplane finite elements having displacement fields based on assumed strains. These satisfy the exact requirements of strain free rigid body modes of displacements. The natural frequencies of simply supported and clamped plates are initially determined when no inplane loads are applied. This showed the influence of the size of the hole on the natural circular frequency. These plates were then subjected to inplane loads and the effect of these forces on the natural frequencies are given. The results show the natural frequencies of square plates with central circular holes decrease with increasing compressive forces, and that the frequencies become zero when the compressive forces are equal to the elastic buckling loads of the plates. By repeating this process for all boundary conditions and applied loads a comprehensive set of results is obtained for the buckling and vibrational properties of square plates containing centrally located holes.

The Influence of the Shape and Rigidity of an Elastic Inclusion on the Transverse Flexure of Thin Plates

1943 ◽  
Vol 10 (2) ◽  
pp. A69-A75
Author(s):  
Martin Goland
Keyword(s):  
Stress Distribution ◽  
Future Study ◽  
Rigid Inclusion ◽  
Elastic Inclusion ◽  
Thin Plates ◽  
Elastic Plates ◽  
Perforated Plates ◽  
Circular Rigid Inclusion ◽  
Special Cases ◽  
Elastic Inclusions

Abstract The purpose of this paper is to investigate the influence of several types of inclusions on the stress distribution in elastic plates under transverse flexure. An “inclusion” is defined as a close-fitting plate of some second material cemented into a hole cut in the interior of the elastic plate. Depending upon the properties of the material of which it is composed, the inclusion is described as rigid or elastic. In particular, the solutions presented will deal with the effects of circular inclusions of differing degrees of elasticity and rigid inclusions of varying elliptical form. Since the rigid inclusion and the hole are limiting types of elastic inclusions, and the circular shape is a special form of the ellipse, plates with either a circular hole or a circular rigid inclusion are important special cases of this discussion. It is hoped that the present analysis of several types of inclusions will aid in a future study of perforated plates stiffened by means of reinforcing rings fitted into the holes.

scholarly journals A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2021 ◽  
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MAT LAB software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

scholarly journals Numerical analysis of stiffened plates subjected to transverse uniform load through the constructal design method

2022 ◽  
Vol 10 (1) ◽  
pp. 99-108 ◽  
Author(s):  
Vinícius Torres Pinto ◽  
Luiz Alberto Oliveira Rocha ◽  
Elizaldo Domingues dos Santos ◽  
Liércio André Isoldi
Keyword(s):  
High Performance ◽  
Design Method ◽  
Material Constant ◽  
Stiffened Plates ◽  
The Finite Element Method ◽  
Uniform Load ◽  
Constructal Design ◽  
Geometric Configurations ◽  
Out Of Plane ◽  
Do So

When it comes to engineering, high performance is always a desired goal. In this context, regarding stiffened plates, the search for better geometric configurations able to minimize the out-of-plane displacements become interesting. So, this study aimed to analyze several stiffened plates defined by the Constructal Design Method (CDM) and solved through the Finite Element Method (FEM) using the ANSYS® software. After that, these plates are compared among each other through the Exhaustive Search (ES) technique. To do so, a non-stiffened rectangular plate was adopted as reference. Then, a portion of its steel volume was converted into stiffeners through the ϕ parameter, which represents the ratio between the volume of the stiffeners and the total volume of the reference plate. Taking into consideration the value of ϕ = 0.3, 75 different stiffened plates arrangements were proposed: 25 with rectangular stiffeners oriented at 0°; 25 with rectangular stiffeners oriented at 45° and 25 with trapezoidal stiffeners oriented at 0°. Maintaining the total volume of material constant, it was investigated the geometry influence on the maximum deflection of these stiffened plates. The results have shown trapezoidal stiffeners oriented at 0° are more effective to reduce the maximum deflections than rectangular stiffeners also oriented at 0°. It was also observed that rectangular stiffeners oriented at 45° presented the smallest maximum deflections for the majority of the analyzed cases, when compared to the trapezoidal and rectangular stiffeners oriented at 0°.

Post-Buckling of Piezoelectric Thin Plates

2015 ◽  
Vol 15 (07) ◽  
pp. 1540020 ◽  
Author(s):  
Michael Krommer ◽  
Hans Irschik
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Nonlinear Behavior ◽  
Dirichlet Boundary Conditions ◽  
Thin Plates ◽  
Governing Equations ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Single Term ◽  
Post Buckling ◽  
Special Case

In the present paper, the geometrically nonlinear behavior of piezoelastic thin plates is studied. First, the governing equations for the electromechanically coupled problem are derived based on the von Karman–Tsien kinematic assumption. Here, the Berger approximation is extended to the coupled piezoelastic problem. The general equations are then reduced to a single nonlinear partial differential equation for the special case of simply supported polygonal edges. The nonlinear equations are approximated by using a problem-oriented Ritz Ansatz in combination with a Galerkin procedure. Based on the resulting equations the buckling and post-buckling behavior of a polygonal simply supported plate is studied in a nondimensional form, where the special geometry of the polygonal plate enters via the eigenvalues of a Helmholtz problem with Dirichlet boundary conditions. Single term as well as multi-term solutions are discussed including the effects of piezoelectric actuation and transverse force loadings upon the solution. Novel results concerning the buckling, snap through and snap buckling behavior are presented.

Study on Flexibility of Intracranial Vascular Stents Based on the Finite Element Method

2018 ◽  
Vol 35 (4) ◽  
pp. 465-474 ◽  
Author(s):  
L. Liu ◽  
H. Jiang ◽  
Y. Dong ◽  
L. Quan ◽  
Y. Tong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cantilever Beam ◽  
Beam Model ◽  
The Finite Element Method ◽  
Simply Supported Beam ◽  
Bending Deformation ◽  
Vascular Stents ◽  
Simply Supported ◽  
Loading Method

ABSTRACTFlexibility is a particularly important biomechanical property for intracranial vascular stents. To study the flexibility of stent, the following work was carried out by using the finite element method: Four mechanical models were adopted to simulate the bending deformation of stents, and comparative studies were conducted about the distinction between cantilever beam and simply supported beam, as well as the distinction between moment-loading method and displacement-loading method. A complete process as implanting a stent including compressing, expanding and bending was also simulated, for analyzing the effects of compressing and expanding deformation on stent flexibility. At the same time, the effects of the arrangement and the number of bridges on stent flexibility were researched. The results show that: 1. A same flexibility index was obtained from cantilever beam model and simply supported beam model; displacement-loading method is better than moment-loading for simulating the bending deformation of stents. 2. The flexibility of stent with compressing and expanding deformation is lower than that in the initial form. 3. Crossly arranging the neighboring bridges in axial direction, can effectively improve the stent flexibility and reduce the flexibility difference in various bending directions; the bridge number, has proportional non-linear correlation with the stent rigidity as well as the maximum moment required for bending the stent.

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