Dependence of Plate-Bending Finite Element Deflections and Eigenvalues on Poisson's Ratio

AIAA Journal ◽  
1974 ◽  
Vol 12 (10) ◽  
pp. 1420-1421 ◽  
Author(s):  
R. NARAYANASWAMI
Keyword(s):  
Finite Element ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Plate Bending

Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio

2016 ◽  
Vol 33 (8) ◽  
pp. 2421-2447 ◽  
Author(s):  
João Paulo Pascon
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Scientific Literature ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Transverse Strain ◽  
Thickness Direction ◽  
Element Analysis ◽  
Content Type

Purpose The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio. Design/methodology/approach The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated. Findings In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution. Originality/value In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented.

scholarly journals Direct Determination of Dynamic Elastic Modulus and Poisson’s Ratio of Timoshenko Rods

Vibration ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 157-173 ◽  
Author(s):  
Guadalupe Leon ◽  
Hung-Liang Chen
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
Elastic Constants ◽  
Frequency Ratio ◽  
Poisson’S Ratio ◽  
Direct Determination ◽  
Poisson's Ratio ◽  
Torsional Mode ◽  
Bending Mode ◽  
Resonance Frequencies

In this paper, the exact solution of the Timoshenko circular beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The exact solution was compared with a 3-D finite element calculation using the ABAQUS program, and the difference between the exact solution and the 3-D finite element method (FEM) was within 0.15% for both the transverse and torsional modes. Furthermore, relationships between the resonance frequencies and Poisson’s ratio were proposed that can directly determine the elastic constants. The frequency ratio between the 1st bending mode and the 1st torsional mode, or the frequency ratio between the 1st bending mode and the 2nd bending mode for any rod with a length-to-diameter ratio, L/D ≥ 2 can be directly estimated. The proposed equations were used to verify the elastic constants of a steel rod with less than 0.36% error percentage. The transverse and torsional frequencies of concrete, aluminum, and steel rods were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of a rod can be determined from the measured frequency ratio quickly and efficiently.

Young's Modulus and Poisson's Ratio Estimation Based on PSO Constriction Factor Method Parameters Evaluation

2019 ◽  
Vol 9 (2) ◽  
pp. 33-46
Author(s):  
George Lucas Dias ◽  
Ricardo Rodrigues Magalhães ◽  
Danton Diego Ferreira ◽  
Bruno Henrique Groenner Barbosa
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Young’S Modulus ◽  
Cantilever Beam ◽  
Poisson’S Ratio ◽  
Inverse Analysis ◽  
Young's Modulus ◽  
Poisson's Ratio ◽  
Factor Method ◽  
Constriction Factor

The knowledge of materials' mechanical properties in design during product development phases is necessary to identify components and assembly problems. These are problems such as mechanical stresses and deformations which normally cause plastic deformation, early fatigue or even fracture. This article is aimed to use particle swarm optimization (PSO) and finite element inverse analysis to determine Young's Modulus and Poisson's ratio from a cantilever beam, manufactured in ASTM A36 steel, subjected to a load of 19.6 N applied to its free end. The cantilever beam was modeled and simulated using a commercial FEA software. Constriction Factor Method (PSO variation) was used and its parameters were analyzed in order to improve errors. PSO results indicated Young's Modulus and Poisson's ratio errors of around 1.9% and 0.4%, respectively, when compared to the original material properties. Improvement in the data convergence and a reduction in the number of PSO iterations was observed. This shows the potentiality of using PSO along with Finite Element Inverse Analysis for mechanical properties evaluation.

scholarly journals 4D Printing of NiTi Auxetic Structure with Improved Ballistic Performance

Micromachines ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 745
Author(s):  
Hany Hassanin ◽  
Alessandro Abena ◽  
Mahmoud Ahmed Elsayed ◽  
Khamis Essa
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Analytical Model ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
4D Printing ◽  
Auxetic Structures ◽  
Negative Poisson's Ratio ◽  
The Impact ◽  
Auxetic Structure

Auxetic structures have attracted attention in energy absorption applications owing to their improved shear modulus and enhanced resistance to indentation. On the other hand, four-dimensional (4D) printing is an emerging technology that is capable of 3D printing smart materials with additional functionality. This paper introduces the development of a NiTi negative-Poisson’s-ratio structure with superelasticity/shape memory capabilities for improved ballistic applications. An analytical model was initially used to optimize the geometrical parameters of a re-entrant auxetic structure. It was found that the re-entrant auxetic structure with a cell angle of −30° produced the highest Poisson’s ratio of −2.089. The 4D printing process using a powder bed fusion system was used to fabricate the optimized NiTi auxetic structure. The measured negative Poisson’s ratio of the fabricated auxetic structure was found in agreement with both the analytical model and the finite element simulation. A finite element model was developed to simulate the dynamic response of the optimized auxetic NiTi structure subjected to different projectile speeds. Three stages of the impact process describing the penetration of the top plate, auxetic structure, and bottom plate have been identified. The results show that the optimized auxetic structures affect the dynamic response of the projectile by getting denser toward the impact location. This helped to improve the energy absorbed per unit mass of the NiTi auxetic structure to about two times higher than that of the solid NiTi plate and five times higher than that of the solid conventional steel plate.

FINITE ELEMENT ANALYSIS OF MECHANICAL DEFORMATION OF CHONDROCYTE TO 2D SUBSTRATE AND 3D SCAFFOLD

2015 ◽  
Vol 15 (05) ◽  
pp. 1550077 ◽  
Author(s):  
JINJU CHEN ◽  
D. L. BADER ◽  
D. A. LEE ◽  
M. M. KNIGHT
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Glass Plate ◽  
Mechanical Deformation ◽  
Poisson's Ratio ◽  
3D Scaffold ◽  
Element Analysis ◽  
Cell Functions

The mechanical properties of cells are important in regulation of many aspects of cell functions. The cell may respond differently to a 2D plate and a 3D scaffold. In this study, the finite element analysis (FEA) was adopted to investigate mechanical deformation of chondrocyte on a 2D glass plate and chondrocyte seeded in a 3D scaffold. The elastic properties of the cell differ in these two different compression tests. This is because that the cell sensed different environment (2D plate and 3D construct) which can alter its structure and mechanical properties. It reveals how the apparent Poisson's ratio of a cell changes with the applied strain depends on its mechanical environment (e.g., the elastic moduli and Poisson's ratios of the scaffold and extracellular matrix) which regulates cell mechanics. In addition, the elastic modulus of the nucleus also plays a significant role in the determination of the Poisson's ratio of the cell for the cells seeded scaffold. It also reveals the intrinsic Poisson's ratio of the cell cannot be obtained by extrapolating the measured apparent Poisson's ratio to zero strain, particularly when scaffold's Poisson's ratio is quite different from the cell.

Poisson's ratio of plywood measured by tension test

Holzforschung ◽  
2009 ◽  
Vol 63 (5) ◽  
Author(s):  
Hiroshi Yoshihara
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Tension Test ◽  
Experimental Results ◽  
Poisson's Ratio ◽  
Element Analysis ◽  
Young’S Moduli ◽  
Tension Tests ◽  
Finite Element Calculations

Abstract In this research, Poisson's ratio of plywood as obtained by a tension test was examined by varying the width of the specimen. The tension tests were conducted on five-plywood of lauan (Shorea sp.) with various widths, and Young's moduli and Poisson's ratios of the specimens were measured. Finite element calculations were independently conducted. A comparison of the experimental results with those of finite element analysis revealed that Young's modulus could be obtained properly when the width of the plywood strip varied. In contrast, the width of the plywood strip should be large enough to determine Poisson's ratio properly.

scholarly journals Piezoelectric materials selection for sensor applications using finite element and multiple attribute decision-making approaches

2015 ◽  
Vol 05 (01) ◽  
pp. 1550003 ◽  
Author(s):  
Anuruddh Kumar ◽  
Anshul Sharma ◽  
Rajeev Kumar ◽  
Rahul Vaish ◽  
Vishal S Chauhan ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Finite Element ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Piezoelectric Materials ◽  
Poisson's Ratio ◽  
Sensor Applications ◽  
Multiple Attribute ◽  
Sensor Structure

This paper examines the selection and performance evaluation of a variety of piezoelectric materials for cantilever-based sensor applications. The finite element analysis method is implemented to evaluate the relative importance of materials properties such as Young's Modulus (E), piezoelectric stress constants (e31), dielectric constant (ε) and Poisson's ratio (υ) for cantilever-based sensor applications. An analytic hierarchy process (AHP) is used to assign weights to the properties that are studied for the sensor structure under study. A technique for order preference by similarity to ideal solution (TOPSIS) is used to rank the performance of the piezoelectric materials in the context of sensor voltage outputs. The ranking achieved by the TOPSIS analysis is in good agreement with the results obtained from finite element method simulation. The numerical simulations show that K 0.5 Na 0.5 NbO 3– LiSbO 3 (KNN–LS) materials family is important for sensor application. Young's modulus (E) is most influencing material's property followed by piezoelectric constant (e31), dielectric constant (ε) and Poisson's ratio (υ) for cantilever-based piezoelectric sensor applications.

Determination of Poisson’s Ratio of Articular Cartilage by Indentation Using Different-Sized Indenters

2004 ◽  
Vol 126 (2) ◽  
pp. 138-145 ◽  
Author(s):  
Hui Jin ◽  
Jack L. Lewis
Keyword(s):  
Finite Element ◽  
Articular Cartilage ◽  
Nonlinear Equation ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Indentation Test ◽  
Test Method ◽  
Poisson's Ratio ◽  
Unconfined Compression

Articular cartilage is often characterized as an isotropic elastic material with no interstitial fluid flow during instantaneous and equilibrium conditions, and indentation testing commonly used to deduce material properties of Young’s modulus and Poisson’s ratio. Since only one elastic parameter can be deduced from a single indentation test, some other test method is often used to allow separate measurement of both parameters. In this study, a new method is introduced by which the two material parameters can be obtained using indentation tests alone, without requiring a secondary different type of test. This feature makes the method more suitable for testing small samples in situ. The method takes advantages of the finite layer effect. By indenting the sample twice with different-sized indenters, a nonlinear equation with the Poisson’s ratio as the only unknown can be formed and Poisson’s ratio obtained by solving the nonlinear equation. The method was validated by comparing the predicted Poisson’s ratio for urethane rubber with the manufacturer’s supplied value, and comparing the predicted Young’s modulus for urethane rubber and an elastic foam material with modulii measured by unconfined compression. Anisotropic and nonhomogeneous finite-element (FE) models of the indentation were developed to aid in data interpretation. Applying the method to bovine patellar cartilage, the tissue’s Young’s modulus was found to be 1.79±0.59MPa in instantaneous response and 0.45±0.26MPa in equilibrium, and the Poisson’s ratio 0.503±0.028 and 0.463±0.073 in instantaneous and equilibrium, respectively. The equilibrium Poisson’s ratio obtained in our work was substantially higher than those derived from biphasic indentation theory and those optically measured in an unconfined compression test. The finite element model results and examination of viscoelastic-biphasic models suggest this could be due to viscoelastic, inhomogeneity, and anisotropy effects.

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