Effective shear modulus of a damaged ply in laminate stiffness analysis: Determination and validation

2019 ◽  
Vol 54 (9) ◽  
pp. 1161-1176
Author(s):  
Mohamed Sahbi Loukil ◽  
Janis Varna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Modulus ◽  
Crack Density ◽  
Accurate Solution ◽  
Effective Stiffness ◽  
Crack Face ◽  
Plane Shear ◽  
Stiffness Reduction ◽  
Element Method

The concept of the “effective stiffness” for plies in laminates containing intralaminar cracks is revisited presenting rather accurate fitting expressions for the effective stiffness dependence on crack density in the ply. In this article, the effective stiffness at certain crack density is back-calculated from the stiffness difference between the undamaged and damaged laminate. Earlier finite element method analysis of laminates with cracked 90-plies showed that the effective longitudinal modulus and Poisson’s ratio of the ply do not change during cracking, whereas the transverse modulus reduction can be described by a simple crack density dependent function. In this article, focus is on the remaining effective constant: in-plane shear modulus. Finite element method parametric analysis shows that the dependence on crack density is exponential and the fitting function is almost independent of geometrical and elastic parameters of the surrounding plies. The above independence justifies using the effective ply stiffness in expressions of the classical laminate theory to predict the intralaminar cracking caused stiffness reduction in laminates with off-axis plies. Results are in a very good agreement with (a) finite element method calculations; (b) experimental data, and (c) with the GLOB-LOC model, which gives a very accurate solution in cases where the crack face opening and sliding displacements are accurately described.

Crack face sliding displacement (CSD) as an input in exact GLOB-LOC expressions for in-plane elastic constants of symmetric damaged laminates

2019 ◽  
Vol 29 (4) ◽  
pp. 547-569 ◽  
Author(s):  
Mohamed Sahbi Loukil ◽  
Janis Varna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Opening Displacement ◽  
Crack Opening ◽  
Crack Density ◽  
Opening Displacement ◽  
Crack Face ◽  
Out Of Plane ◽  
Crack Sliding Displacement ◽  
Element Method

The crack opening and crack sliding displacements of both faces of an intralaminar crack are the main parameters defining the significance of each crack in laminate stiffness degradation, according to the previously published GLOB-LOC approach for symmetric laminates with an arbitrary number of cracks in all plies. In the exact stiffness expressions of this approach, the crack density is always multiplied by crack opening displacement and crack sliding displacement. The dependence of crack opening displacement on geometrical and elastic parameters of adjacent plies was studied previously and described by simple fitting functions. The crack sliding displacement has been analyzed for low-crack densities only and the proposed finite element method-based fitting expressions are oversimplified not including the out-of-plane ply stiffness effects. Based on finite element method analysis, more accurate expressions for so-called non-interactive cracks are suggested in the presented article. For the first time the shear stress perturbations are analyzed and interaction functions are presented with the feature that they always lead to slightly conservative predictions. The presented simple fitting functions, when used in the GLOB-LOC model, give predictions that are in a good agreement with finite element method results and with experimental data for laminates with damaged off-axis plies in cases when crack face sliding is of importance. The significance of including crack sliding displacement in stiffness predictions is demonstrated.

Finite Element Method for Stochastic Beams Based on Variational Principles

1997 ◽  
Vol 64 (3) ◽  
pp. 664-669 ◽  
Author(s):  
Y.-J. Ren ◽  
I. Elishakoff ◽  
M. Shinozuka
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Covariance Function ◽  
Variational Principles ◽  
Joint Probability ◽  
Accurate Solution ◽  
Joint Probability Distribution ◽  
Covariance Functions ◽  
The Mean ◽  
Element Method

This paper proposes a new version (fundamentally different from the existing ones) of finite element method for the mean and covariance functions of the displacement for bending beams with spatially random stiffness. Apart from the conventional finite element method for stochastic problems, which utilizes either perturbation or series expansion technique or the Monte Carlo simulation, the present method is based on the newly established variational principles. The finite element scheme is formulated directly with respect to the mean function and covariance function, rather than perturbed components of the displacement. It takes into account an information on joint probability distribution function of the random stiffness to obtain the covariance function of the displacement. Therefore, the accurate solution can be obtained even if the coefficient of variation of the random stiffness is large, in contrast to conventional technique. Several examples are given to illustrate the advantage of the proposed method, compared with the conventional ones.

scholarly journals A HYBRID SMOOTHED FINITE ELEMENT METHOD (H-SFEM) TO SOLID MECHANICS PROBLEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 1340011 ◽  
Author(s):  
XU XU ◽  
YUANTONG GU ◽  
GUIRONG LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strain Energy ◽  
Solid Mechanics ◽  
Weighted Average ◽  
Accurate Solution ◽  
Numerical Studies ◽  
Smoothed Finite Element Method ◽  
Theoretical Results ◽  
Element Method

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter α is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper- and lower-bound solutions can always be obtained by adjusting α; (2) there exists a preferable α at which the H-SFEM can produce the ultrasonic accurate solution.

Global Multiscale Finite Element Method for Flow in Fractured Media

2014 ◽  
Vol 945-949 ◽  
pp. 1007-1010
Author(s):  
Xiao Lin Li ◽  
Guang Wei Meng ◽  
Li Ming Zhou ◽  
Feng Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
Accurate Solution ◽  
Fractured Media ◽  
Fine Scale ◽  
Multiscale Finite Element Method ◽  
Dual Porosity Model ◽  
Multiscale Finite Element ◽  
Element Method

Numerical simulation in fractured media is challenging because of the complex microstructure and the coupled fluid flow in porous and fractured media. In this paper, we have extended the global multiscale finite element method (GMsFEM) to study the fluid flow in fractured media with a dual porosity model. By using the fine-scale solution at t=0 to determine the boundary conditions of the basis function, local and nonlocal informations are reflected in the basis functions. As a result, an accurate solution can be achieved in the coarse scale. Numerical example demonstrate that the solution of GMsFEM is highly consistent with the fine-scale solution of FEM. Furthermore, GMsFEM provides a great computational efficiency.

Micro-mechanical analysis of the pineapple-reinforced polymeric composite by the inclusion of pineapple leaf particulates

2021 ◽  
pp. 146442072199085
Author(s):  
Abir Saha ◽  
Santosh Kumar ◽  
Divya Zindani ◽  
Sumit Bhowmik
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Polymeric Composites ◽  
Fiber Reinforced ◽  
Plane Shear ◽  
Pineapple Leaf Fiber ◽  
Outer Plane ◽  
Leaf Fiber ◽  
Element Method

The present study is focused on investigating the effect of the micro-mechanical properties of the natural fiber- (pineapple leaf fiber) reinforced polymeric composites by the addition of pineapple leaf micro-particulates. For the investigation, a two-step approach has been used. In the first step, finite element method-based analysis has been used to characterize the tensile and shear properties of the pineapple leaf fiber-reinforced polymeric composites (FRP) and pineapple paticulate-reinforced polymeric composites (PRC), and the adopted finite element method-based analysis has been validated through the experimental approach. In the second step, the validated finite element method-based analysis has been used to characterize the micro-mechanical properties of the hybrid fiber-reinforced polymeric composites (HFRP) fabricated using the pineapple leaf micro-particle embedded epoxy as a matrix material and the pineapple leaf fiber has been used as reinforcing material. It has been observed through the analysis that the micro-mechanical properties of HFRP were superior to that of FRP. There has been a 10.16% increment in Young’s modulus in the longitudinal direction and a 26.36% increment in Young’s modulus in the transverse direction for HFRP over FRP. Further, a 9.91% increment for in-plane shear modulus and 26.17% increment in outer-plane shear modulus have been observed for HFRP in comparison to FRP. These results suggest that pineapple leaf particulates are good reinforcing materials to enhance the transverse direction and outer plane micro-mechanical properties of the fiber-reinforced composite.

Modified Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Structural Analysis - Part 1: Continual and Discrete-Continual Formulations of the Problems

2014 ◽  
Vol 670-671 ◽  
pp. 720-723 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Accurate Solution ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Boundary Problems ◽  
Piecewise Constant ◽  
Element Method

The distinctive paper is devoted to wavelet-based discrete-continual finite element method (WDCFEM) of structural analysis. Two-dimensional and three-dimensional problems of analysis of structures with piecewise constant physical and geometrical parameters along so-called “basic” direction are under consideration. High-accuracy solution of the corresponding problems at all points of the model is not required normally, it is necessary to find only the most accurate solution in some pre-known local domains. Wavelet analysis is a powerful and effective tool for corresponding researches. Initial continual and discrete-continual formulations of multipoint boundary problems of two-dimensional and three-dimensional structural analysis are presented.

Analysis on Torsional Vibration Characteristics of Turbo-Generator Units Based on Finite Element Method

2014 ◽  
Vol 915-916 ◽  
pp. 22-25
Author(s):  
Xi He ◽  
Yu Jiong Gu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Torsional Vibration ◽  
Power Grid ◽  
Safety Evaluation ◽  
Accurate Solution ◽  
Vibration Characteristics ◽  
Fe Model ◽  
Turbo Generator ◽  
Element Method

The torsional vibration problems of turbo-generator shafts are increasing widespread and sever under the coupled action between the turbo-generator unit and the power grid because of the complicated power grid structure. Thus, the accurate solution of torsional vibration inherent characteristics of the shafts is of great significance to do the safety evaluation. The finite element method (FEM) with higher accuracy is adopted to calculate the torsional vibration inherent characteristics in this paper. A 1000 MW turbo-generator shaft is taken as a studying object and its torsional vibration finite element (FE) model and solving process are introduced, using ANSYS software as implementation platform of the FEM. The simulation results show that the torsional vibration characteristics calculated by FEM are accurate and reliable.

Sign in / Sign up

Export Citation Format

Share Document