Dispersion of Waves in Composite Laminates With Transverse Matrix Cracks, Finite Element and Plate Theory Computations

1998 ◽  
Vol 65 (3) ◽  
pp. 588-595
Author(s):  
M. A˚berg ◽  
P. Gudmundson
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Composite Laminates ◽  
Plate Theory ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Finite Element Program ◽  
Periodic Cell ◽  
Matrix Cracks

Dispersion relations for laminated composite plates with transverse matrix cracks have been computed using two methods. In the first approach it is assumed that the matrix cracks appear periodically and hence it is possible to consider a periodic cell of the structure using Bloch-type boundary conditions. This problem was formulated in complex notation and solved in a standard finite element program (ABAQUS) using two identical finite element meshes, one for the real part and one for the imaginary part of the displacements. The two meshes were coupled by the boundary conditions on the cell. The code then computed the eigenfrequeneies of the system for a given wave vector. It was then possible to compute the phase velocities. The second approach used may be viewed as a two step homogenization. First the cracked layers are homogenized and replaced by weaker uncracked layers and then the standard first-order shear-deformation laminate theory is used to compute dispersion relations. Dispersion relations were computed using both methods for three glass-fiberepoxy laminates ([0/90]2,[0/90]sand[0/45/-45]s with cracks in the 90 and ±45 deg plies). For the lowestflexural mode the difference in phase velocity between the methods was less then five percent for wavelengths longer than two times the plate thickness. For the extensional mode a wavelength often plate thicknesses gave a five percent difference.

scholarly journals Antiplane–inplane shear mode delamination between two second-order shear deformable composite plates

2016 ◽  
Vol 22 (3) ◽  
pp. 259-282 ◽  
Author(s):  
András Szekrényes
Keyword(s):  
Plate Theory ◽  
Plate Thickness ◽  
State Space Model ◽  
Boundary Surface ◽  
Plate Boundary ◽  
Composite Plates ◽  
Second Order ◽  
Shear Mode ◽  
Mode Iii ◽  
Double Plate System

The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton’s principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.

Modes of Wave Propagation and Dispersion Relations in Inclusion Reinforced Composite Plates

2010 ◽  
Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang
Keyword(s):  
Composite Plate ◽  
Elastic Moduli ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Elastic Behavior ◽  
Effective Elastic Moduli ◽  
Aspect Ratios ◽  
Reinforced Composite

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.

scholarly journals Monte Carlo Simulations of Coupled Transient Seepage Flow and Soil Deformation in Levees

2020 ◽  
Vol 21 (1) ◽  
pp. 147-156
Author(s):  
Fred Thomas Tracy ◽  
Jodi L. Ryder ◽  
Martin T. Schultz ◽  
Ghada S. Ellithy ◽  
Benjamin R. Breland ◽  
...  
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Boundary Conditions ◽  
High Performance ◽  
Hurricane Ike ◽  
Finite Element Program ◽  
Conservation Of Mass ◽  
Total Head ◽  
Element Program ◽  
Finite Element Node

The purpose of this research is to compare the results from two different computer programs of flow analysesof two levees at Port Arthur, Texas where rising water of a flood from Hurricane Ike occurred on the levees. The first program (Program 1) is a two-dimensional (2-D) transient finite element program that couples the conservation of mass flow equation with accompanying hydraulic boundary conditions with the conservation of force equations with accompanying x and y displacement and force boundary conditions, thus yielding total head, x displacement, and y displacement as unknowns at each finite element node. The second program (Program 2) is a 2-D transient finite element program that considers only the conservation of mass flowequation with its accompanying hydraulic boundary conditions, yielding only total head as the unknown at each finite element node. Compressive stresses can be computed at the centroid of each finite element when using the coupled program. Programs 1 and 2 were parallelized for high performance computing to consider thousands of realisations of the material properties. Since a single realisation requires as much as one hour of computer time for certain levees, the large realisation computation is made possible by utilising HPC. This Monte Carlo type analysis was used to compute the probability of unsatisfactory performance for under seepage, through seepage, and uplift for the two levees. Respective hydrographs from the flood resulting from Hurricane Ike were applied to each levee. When comparing the computations from the two programs, the most significant result was the two programs yielded significantly different values in the computed results in the two clay levees considered in this research.  

Estimation of Residual Stresses in Steel Welded Joints Using Three Dimensional Finite Element Analysis

2018 ◽  
Author(s):  
Shivdayal Patel ◽  
B. P. Patel ◽  
Suhail Ahmad
Keyword(s):  
Residual Stress ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Residual Stresses ◽  
Boundary Conditions ◽  
Welding Speed ◽  
Welded Joints ◽  
Plate Thickness ◽  
Welding Process ◽  
Element Analysis

Welding is one of the most used joining methods in the ship industry. However, residual stresses are induced in the welded joints due to the rapid heating and cooling leading to inhomogenously distributed dimensional changes and non-uniform plastic and thermal strains. A number of factors, such as welding speed, boundary conditions, weld geometry, weld thickness, welding current/voltage, number of weld passes, pre-/post-heating etc, influence the residual stress distribution. The main aim of this work is to estimate the residual stresses in welded joints through finite element analysis and to investigate the effects of boundary conditions, welding speed and plate thickness on through the thickness/surface distributions of residual stresses. The welding process is simulated using 3D Finite element model in ABAQUS FE software in two steps: 1. Transient thermal analysis and 2. Quasi-static thermo-elasto-plastic analysis. The normal residual stresses along and across the weld in the weld tow region are found to be significant with nonlinear distribution. The residual stresses increase with the increase in the thickness of the plates being welded. The nature of the normal residual stress along the weld is found to be tensile-compressive-tensile and the nature of normal residual stress across the weld is found to be tensile along the thickness direction.

Analysis of Symmetric Angle-Ply Laminated Composite Skew Plates Using Hybrid Trefftz Finite Element

2019 ◽  
Author(s):  
Subhasankar Dwibedi
Keyword(s):  
Finite Element ◽  
Composite Structures ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Point Load ◽  
Shear Stresses ◽  
Skew Angle ◽  
Distributed Load ◽  
Trefftz Finite Element

Abstract Analysis of symmetric angle-ply skew laminated composite plates has been presented in the study using a newly developed hybrid Trefftz finite element (hTFE). Mindlin’s plate theory has been used to develop the present hTFE. The forms of displacement are assumed such that governing partial differential equations are satisfied a priori inside the element domain. Particular solutions of the governing equations have been ignored and Trefftz functions are derived using the homogenous solutions only. Inter-element continuity has been established by employing another displacement field along the edges of the hTFEs. The transverse shear stresses have been ignored at the top and bottom surfaces of the laminate. The angle of inclination of the width of the plate with the y-axis has been taken as the skew angle and different forms of skew plates are obtained by varying the skew angle. Sinusoidally distributed load (SDL), uniformly distributed load (UDL), and point load (PL) have been subjected to the top surface of the laminate and the non-dimensionalized center point deflection have been evaluated to assess the performance of the present hTFE. The observation from the present study further reinforce the versatility of the hTFE method for analysis of composite structures with complex shapes or geometries.

Predicting the Impact of Quenching on Mechanical Properties of Complex-Shaped Aluminum Alloy Parts

1995 ◽  
Vol 117 (2) ◽  
pp. 479-488 ◽  
Author(s):  
D. D. Hall ◽  
I. Mudawar
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Aluminum Alloy ◽  
Boundary Conditions ◽  
Finite Element Program ◽  
Part Geometry ◽  
Heat Treated ◽  
Element Program ◽  
Nozzle Configuration ◽  
The Impact

The mechanical properties of age-hardenable aluminum alloy extrusions are critically dependent on the rate at which the part is cooled (quenched) after the forming operation. The present study continues the development of an intelligent spray quenching system, which selects the optimal nozzle configuration based on part geometry and composition such that the magnitude and uniformity of hardness (or yield strength) is maximized while residual stresses are minimized. The quenching of a complex-shaped part with multiple, overlapping sprays was successfully modeled using spray heat transfer correlations as boundary conditions within a finite element program. The hardness distribution of the heat-treated part was accurately predicted using the quench factor technique; that is, the metallurgical transformations that occur within the part were linked to the cooling history predicted by the finite element program. This study represents the first successful attempt at systematically predicting the mechanical properties of a quenched metallic part from knowledge of only the spray boundary conditions.

A Finite Element Solution for Fully Intrinsic Plate Theory

2014 ◽  
Author(s):  
Zahra Sotoudeh
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Plate Theory ◽  
General Purpose ◽  
Flexible Body ◽  
Element Formulation ◽  
Element Solution ◽  
Beam Equations ◽  
Linear Version ◽  
Rotation Parameters

The fully intrinsic equations for plates (and analogous ones for shells), although equally as elegant as the corresponding beam equations, have neither been used for general-purpose finite element nor multi-flexible-body analysis. The fully intrinsic equations for plates have the same advantages of fully intrinsic equations for beams. These equations are geometrically exact, the highest order of nonlinearities is only of second order, and they do not include rotation parameters. We present a finite element formulation for these equations, and then investigate different possible boundary conditions and loading situations on simplified linear version.

A NEW TRIANGULAR ELEMENT BASED ON HIGHER ORDER SHEAR DEFORMATION THEORY FOR FLEXURAL VIBRATION OF COMPOSITE PLATES

2002 ◽  
Vol 02 (02) ◽  
pp. 163-184 ◽  
Author(s):  
A. CHAKRABARTI ◽  
A. H. SHEIKH
Keyword(s):  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Higher Order ◽  
Triangular Element

A triangular element based on Reddy's higher order shear deformation theory is developed for free vibration analysis of composite plates. In the Reddy's plate theory, the transverse shear stress varies in a parabolic manner across the plate thickness and vanishes at the top and bottom surfaces of the plate. Moreover, it does not involve any additional unknowns. Thus the plate theory is quite simple and elegant. Unfortunately, such an attractive plate theory cannot be exploited as expected in finite element analysis, primarily due to the difficulties in satisfying the inter-element continuity requirement. This has inspired us to develop the present element, which has three corner nodes and three mid-side nodes with the same number of degrees of freedom. To demonstrate the performance of the element, numerical examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical solutions and other published results, which show the accuracy and range of applicability of the proposed element in the problem of vibration analysis.

Analytical Solutions of Refined Plate Theories of Cross-Ply Composite Laminates

1991 ◽  
Vol 113 (4) ◽  
pp. 570-578 ◽  
Author(s):  
A. A. Khdeir ◽  
J. N. Reddy
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Composite Laminates ◽  
Laminated Composite ◽  
Composite Plates ◽  
Third Order ◽  
State Space Approach ◽  
Various Boundary Conditions ◽  
Shear Deformation Theories ◽  
Space Approach

Exact solutions of rectangular laminated composite plates with different boundary conditions are studied. The Le´vy-type solutions of the classical, first-order and third-order shear deformation theories are developed using the state-space approach. The finite-element solutions for the three theories are also computed and compared with the exact solutions for various boundary conditions.

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