Wrinkling of a Polymeric Gel During Transient Swelling

2015 ◽  
Vol 82 (6) ◽  
Author(s):  
William Toh ◽  
Zhiwei Ding ◽  
Teng Yong Ng ◽  
Zishun Liu
Keyword(s):  
Finite Element ◽  
Time Dependence ◽  
Wave Number ◽  
Inverse Relation ◽  
Critical Wave Number ◽  
Interesting Phenomenon ◽  
State Space Methods ◽  
Compressive Stresses ◽  
Free Swelling ◽  
Geometrical Constraints

When exposed to an external solvent, a dry polymeric network imbibes the solvent and undergoes large deformation. The resulting aggregate is known as a hydrogel. This swelling process is diffusion driven and thus results in differential swelling during transient swelling. When subjected to external geometrical constraints, such as being rigidly fixed or attachment to a compliant substrate, wrinkles have been shown to appear due to mechanical instabilities. In the case of free swelling, there are no external constraints to induce the instabilities accounting for wrinkling patterns. However, during the transient swelling process, the swelling differential between the gel on the exterior and the interior causes compressive stresses and gives rise to mechanical instabilities. It is also observed that the time dependence of the swelling profile causes the wrinkles to evolve with time. In this work, we investigate this interesting phenomenon of transient wrinkle mode evolution using the finite element and state-space methods. From our simulations and prediction, we find that there is an inverse relation between critical wave number and time, which has earlier been observed in experiments.

scholarly journals Fractographical Analysis and Biomechanical Considerations of a Tooth Restored With Intracanal Fiber Post: Report of the Fracture and Importance of the Fiber Arrangements

2016 ◽  
Vol 41 (5) ◽  
pp. E149-E158 ◽  
Author(s):  
VF Wandscher ◽  
CD Bergoli ◽  
IF Limberger ◽  
TP Cenci ◽  
P Baldissara ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Glass Fiber ◽  
Shear Stresses ◽  
Fiber Post ◽  
Element Analysis ◽  
Parallel Fibers ◽  
Tooth Structure ◽  
Anterior Teeth ◽  
Compressive Stresses

SUMMARY Objective: This article aims to present a fractographic analysis of an anterior tooth restored with a glass fiber post with parallel fiber arrangement, taking into account force vectors, finite element analysis, and scanning electron microscopy (SEM). Methods: A patient presented at the Faculty of Dentistry (Federal University of Santa Maria, Brazil) with an endodontically treated tooth (ETT), a lateral incisor that had a restorable fracture. The treatment was performed, and the fractured piece was analyzed using stereomicroscopy, SEM, and finite element analysis. Results: The absence of remaining coronal tooth structure might have been the main factor for the clinical failure. We observed different stresses actuating in an ETT restored with a fiber post as well as their relationship with the ultimate fracture. Tensile, compression, and shear stresses presented at different levels inside the restored tooth. Tensile and compressive stresses acted together and were at a maximum in the outer portions and a minimum in the inner portions. In contrast, shear stresses acted concomitantly with tensile and compressive stresses. Shear was higher in the inner portions (center of the post), and lower in the outer portions. This was confirmed by finite element analysis. The SEM analysis showed tensile and compression areas in the fiber post (exposed fibers=tensile areas=lingual surface; nonexposed fibers=compression areas=buccal surface) and shear areas inside the post (scallops and hackle lines). Stereomicroscopic analysis showed brown stains in the crown/root interface, indicating the presence of microleakage (tensile area=lingual surface). Conclusion: We concluded that glass fiber posts with parallel fibers (0°), when restoring anterior teeth, present a greater fracture potential by shear stress because parallel fibers are not mechanically resistant to support oblique occlusal loads. Factors such as the presence of remaining coronal tooth structure and occlusal stability assist in the biomechanical equilibrium of stresses that act upon anterior teeth.

A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate

2006 ◽  
Vol 128 (4) ◽  
pp. 477-488 ◽  
Author(s):  
A. Chakraborty ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Shear Deformation ◽  
Mechanical Response ◽  
Laminated Composite ◽  
Wave Number ◽  
Single Element ◽  
Element Formulation ◽  
Frequency Wave ◽  
Spectral Finite Element

A new spectral plate element (SPE) is developed to analyze wave propagation in anisotropic laminated composite media. The element is based on the first-order laminated plate theory, which takes shear deformation into consideration. The element is formulated using the recently developed methodology of spectral finite element formulation based on the solution of a polynomial eigenvalue problem. By virtue of its frequency-wave number domain formulation, single element is sufficient to model large structures, where conventional finite element method will incur heavy cost of computation. The variation of the wave numbers with frequency is shown, which illustrates the inhomogeneous nature of the wave. The element is used to demonstrate the nature of the wave propagating in laminated composite due to mechanical impact and the effect of shear deformation on the mechanical response is demonstrated. The element is also upgraded to an active spectral plate clement for modeling open and closed loop vibration control of plate structures. Further, delamination is introduced in the SPE and scattered wave is captured for both broadband and modulated pulse loading.

A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number

2017 ◽  
Vol 22 (1) ◽  
pp. 133-156 ◽  
Author(s):  
Yu Du ◽  
Zhimin Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
Phase Error ◽  
Three Dimensions ◽  
Wave Number ◽  
Weak Galerkin ◽  
High Wave Number ◽  
Large Wave ◽  
Element Method

AbstractWe study the error analysis of the weak Galerkin finite element method in [24, 38] (WG-FEM) for the Helmholtz problem with large wave number in two and three dimensions. Using a modified duality argument proposed by Zhu and Wu, we obtain the pre-asymptotic error estimates of the WG-FEM. In particular, the error estimates with explicit dependence on the wave numberkare derived. This shows that the pollution error in the brokenH1-norm is bounded byunder mesh conditionk7/2h2≤C0or (kh)2+k(kh)p+1≤C0, which coincides with the phase error of the finite element method obtained by existent dispersion analyses. Herehis the mesh size,pis the order of the approximation space andC0is a constant independent ofkandh. Furthermore, numerical tests are provided to verify the theoretical findings and to illustrate the great capability of the WG-FEM in reducing the pollution effect.

An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang ◽  
Jianhui Wang
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Higher Order ◽  
Wave Number ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Circular Cylindrical Shells ◽  
Geometrical Factors ◽  
Circumferential Wave

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

Finite Element Analysis for Wave Spring of Multi-Disc Wet Clutch Based on ANSYS

2013 ◽  
Vol 419 ◽  
pp. 203-208
Author(s):  
Ying Yu ◽  
Yao Run Peng ◽  
Shi Xin Lan ◽  
Ping Zhou
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Structural Characteristics ◽  
Response Speed ◽  
Wave Number ◽  
Element Analysis ◽  
Wet Clutch ◽  
Relationship Of ◽  
Deformation Relationship

Wave spring is a key component of multi-disc wet clutch and the response speed and running quality of multi-disc wet clutch is affected by its characteristics. This paper analyses the theoretical calculation of load-deformation relationship of wave spring. The load-deformation relationship of wave spring is obtained by ANSYS10.0 software according to its structural characteristics and actual boundary condition and compared with the calculated results based on different methods and the measured value, and then study the effect of the wave number on the load-deformation relationship of wave spring. The results show that the calculated value of finite element analysis (FEM) is closer to the measured value and the FEM has more advantages on simulation of the working performance of wave spring.

Effects of Configuration on Plastic Package Stresses

1991 ◽  
Vol 113 (4) ◽  
pp. 397-404 ◽  
Author(s):  
L. T. Nguyen ◽  
S. A. Gee ◽  
W. F. v. d. Bogert
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Stress Reduction ◽  
Stress Profile ◽  
Strain Gages ◽  
Molding Compounds ◽  
Compressive Stresses ◽  
Plastic Packages ◽  
Plastic Package ◽  
Element Simulation

This paper examines the effects of device and leadframe configurations on the stresses encountered in typical Dual-in-Line plastic packages. The parameters studied include the die size, the die pad size, the location of the die with respect to the die pad center, and the die coating configuration. Special piezoresistive strain gages deposited on dies of varying sizes are used to map the stress profile across the die surfaces after molding. Finite element simulation of these effects is also conducted. Results indicate that the compressive stresses from the molding compounds are governed with diminishing influence by the size of the die. Furthermore, rather high compressive stresses are observed in the vicinity of the edges of large dies. More subtle effects are found for the influence of the die pad size, the aspect ratio of the die, and the extent of the die offsetting with respect to the die pad center. Finally, by surrounding the die with a thin trail of silicone gel to provide for lateral cushioning, stress reduction is slightly more effective than in the standard “glob-top” coating.

scholarly journals Effects of Suction–Injection–Combination (SIC) on the onset of Rayleigh–Bénard Electroconvection in a Micropolar Fluid

2015 ◽  
Vol 14 (3) ◽  
pp. 23-42 ◽  
Author(s):  
S Pranesh ◽  
Tarannum Sameena ◽  
Baby Riya
Keyword(s):  
Stability Analysis ◽  
Micropolar Fluid ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Wave Number ◽  
Critical Wave Number ◽  
Onset Of Convection ◽  
Temperature Boundary ◽  
The Stability ◽  
Rayleigh Benard

The effect of Suction – injection combination on the onset of Rayleigh – Bénard electroconvection micropolar fluid is investigated by making a linear stability analysis. The Rayleigh-Ritz technique is used to obtain the eigenvalues for different velocity and temperature boundary combinations. The influence of various parameters on the onset of convection has been analysed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC being pro-gravity or anti-gravity. A similar Pe-sensitivity is found in respect of the critical wave number. It is observed that the fluid layer with suspended particles heated from below is more stable compared to the classical fluid layer without suspended particles.

Further Studies to Evaluate Crack Opening Areas for Through-Wall Cracks in the Vicinity of Welded Attachments

2010 ◽  
Author(s):  
J. K. Sharples ◽  
C. J. Madew ◽  
R. Charles ◽  
P. J. Budden
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Complex Geometry ◽  
Crack Opening ◽  
Stress Profile ◽  
Finite Element Models ◽  
Compressive Stresses ◽  
Displacement Theory ◽  
Plate Geometry

A paper was presented at the 2009 ASME PVP Conference on evaluating, by finite element techniques, crack opening area (COA) and stress intensity factor, KI, values for through-wall cracks located in the region where an attachment is welded to a plate geometry. Both membrane and bend loads were considered. In addition, based on the stress profile in the un-cracked complex geometry over the region where the cracks would be introduced, COA and KI values were evaluated for the same crack sizes located in a simple plate geometry. This enabled information to be established on the conservatism, or otherwise, of using simple plate solutions to evaluate COA and KI for cracks in the complex geometry. The present paper reports on further studies that have been undertaken to investigate the effect on the previous COA and KI results of considering (i) large displacement theory which may be important for combined membrane and bend loading, and (ii) contact elements in the finite element models since in the previous studies, the mesh was allowed to “overlap on itself” when crack closure was evident due to compressive stresses during bend loading.

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