scholarly journals Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

2020 ◽  
Vol 42 (3) ◽  
pp. 239-254
Author(s):  
A. Pagani ◽  
R. Azzara ◽  
R. Augello ◽  
E. Carrera ◽  
B. Wu
Keyword(s):  
Three Dimensional ◽  
Path Following ◽  
Higher Order ◽  
Large Displacement ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Displacement Fields ◽  
Isotropic Shell ◽  
Geometrical Nonlinear ◽  
Lagrange Strain

The present paper presents the evaluation of three-dimensional (3D) stress distributions of shell structures in the large displacement and rotation fields. The proposed geometrical nonlinear model is based on a combination of the Carrera Unified Formulation (CUF) and the Finite Element Method (FEM). Besides, a Newton-Raphson linearization scheme is adopted to compute the geometrical nonlinear equations, which are constrained using the arc-length path-following method. Static analyses are performed using refined models and the full Green-Lagrange strain-displacement relations. The Second Piola-Kirchhoff (PK2) stress distributions are evaluated, and lower- to higher-order expansions are employed. Popular benchmarks problems are analyzed, including cylindrical isotropic shell structure with various boundary and loading conditions. Various numerical assessments for different equilibrium conditions in the moderate and large displacement fields are proposed. Results show the distribution of axial and shear stresses, varying the refinement of the proposed two-dimensional (2D) shell model. It is shown that for axial components, a lower-order expansion is sufficient, whereas a higher-order one is needed to accurately predict shear stresses.

A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

2017 ◽  
Vol 21 (6) ◽  
pp. 1820-1842
Author(s):  
Wu Zhen ◽  
Ma Rui ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Higher Order ◽  
Triangular Element ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Shear Stress ◽  
Transverse Shear Stresses ◽  
Derivatives Of

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

scholarly journals Implementation of Virtual Crack Closure Technique for Damaged Composite Plates Using Higher-Order Layerwise Model

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Kwang S. Woo ◽  
Jae S. Ahn
Keyword(s):  
Crack Closure ◽  
Edge Crack ◽  
Present Model ◽  
Three Dimensional ◽  
Higher Order ◽  
Virtual Crack Closure Technique ◽  
Single Edge ◽  
Displacement Fields ◽  
Closure Technique ◽  
Aluminum Plates

A higher-order layerwise model is proposed to determine stress intensity factors using virtual crack closure technique for single-edge-crack aluminum plates with patch repairs. The present method is based onp-convergent approach and adopts the concept of subparametric elements. In assumed displacement fields, strain-displacement relations and three-dimensional constitutive equations of layers are obtained by combination of two- and one-dimensional shape functions. Thus, it allows independent implementation ofp-refinement for in-plane and transversal displacements. In the proposed elements, the integrals of Legendre polynomials and Gauss-Lobatto technique are employed to interpolate displacement fields and to implement numerical quadrature, respectively. For verification of the present model, not only single-edge-crack plates but also V-notch aluminum plates are first analyzed. For patched aluminum plate with behavior of complexity, the accuracy and simplicity of the present model are shown with comparison of the results with previously published papers using the conventional three-dimensional finite elements based onh-refinement.

Three-dimensional deformations in a single-lap joint

1994 ◽  
Vol 29 (2) ◽  
pp. 137-145 ◽  
Author(s):  
M Y Tsai ◽  
J Morton
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Lap Joint ◽  
Displacement Fields ◽  
Element Analysis ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Effects ◽  
Peel Stress

The three-dimensional nature of the state of deformation in a single-lap test specimen is investigated in a linear elastic finite element analysis in which the boundary conditions account for the geometrically non-linear effects. The validity of the model is demonstrated by comparing the resulting displacement fields with those obtained from a moiré inteferometry experiment. The three-dimensional adherend and adhesive stress distributions are calculated and compared with those from a two-dimensional non-linear numerical analysis, Goland and Reissner's solution, and experimental measurements. The nature of the three-dimensional mechanics is described and discussed in detail. It is shown that three-dimensional regions exists in the specimen, where the adherend and adhesive stress distributions in the overlap near (and especially on) the free surface are quite different from those occurring in the interior. It is also shown that the adhesive peel stress is extremely sensitive to this three-dimensional effect, but the adhesive shear is not. It is also observed that the maximum value of the peel stress occurs at the end of the overlap in the central two-dimensional core region, rather than at the corners where the three-dimensional effects are found. The extent of three-dimensional regions is also quantified.

Vibration characteristic of laminated sandwich plates with soft core based on an improved higher-order zigzag theory

2008 ◽  
Vol 222 (8) ◽  
pp. 1443-1452 ◽  
Author(s):  
M K Pandit ◽  
A H Sheikh ◽  
B N Singh
Keyword(s):  
Transverse Shear ◽  
Plate Theory ◽  
Three Dimensional ◽  
Higher Order ◽  
Thickness Variation ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Displacement ◽  
Zigzag Theory ◽  
Three Dimensional Elasticity

This paper presents an improved higher order zigzag theory for vibration of laminated sandwich plates. It ensures continuity of transverse shear stresses at all the layer interfaces and transverse shear stress-free condition at the top and bottom surfaces apart from core compressibility. The through-thickness variation of in-plane displacements is assumed to be cubic, whereas transverse displacement varies quadratically across the core, which is modelled as a three-dimensional elastic continuum. An efficient C0 finite element is developed for the implementation of the plate theory. The model is validated using three-dimensional elasticity solutions and some other relevant results available in the literature.

Influence of Mechanical Behavior of Adhesives on Shear Stress Distributions in the Single-Lap Adhesive Joints

2011 ◽  
Vol 306-307 ◽  
pp. 1126-1129
Author(s):  
Xiao Cong He
Keyword(s):  
Shear Stress ◽  
Mechanical Behavior ◽  
Three Dimensional ◽  
Viscoelastic Behavior ◽  
Adhesive Layer ◽  
Adhesive Joints ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Element Analysis ◽  
Three Dimensional Finite Element

This paper deals with the effects of mechanical behavior of adhesives on the shear stress distributions of single-lap adhesive joints under tension using the three-dimensional finite element analysis (FEA) technique. Numerical examples are provided to show the influence on the shear stresses of the joints using adhesives of different characteristics which encompass the entire spectrum of viscoelastic behavior. FEA solutions of the shear stress distributions in the adhesive layer have been obtained for four typical characteristics of adhesives. The results indicate that Young’s modulus and Poisson’s ratios of adhesives strongly affect the shear stress distributions of the joints.

A Higher-Order Theory for Plane Stress Conditions of Laminates Consisting of Isotropic Layers

1999 ◽  
Vol 66 (1) ◽  
pp. 95-100 ◽  
Author(s):  
X. J. Wu ◽  
S. M. Cheng
Keyword(s):  
Three Dimensional ◽  
Order Theory ◽  
Higher Order ◽  
Shear Stresses ◽  
Stress Equilibrium ◽  
Material Discontinuities ◽  
Interlaminar Shear ◽  
Higher Order Theory ◽  
Three Dimensional Elasticity ◽  
Higher Order Functions

In this paper, a higher-order theory is derived for laminates consisting of isotropic layers, on the basis of three-dimensional elasticity with displacements as higher-order functions of z in the thickness direction. The theory employs three stress potentials, Ψ (an Airy function), p (a harmonic function), and its conjugate q, to satisfy all conditions of stress equilibrium and compatibility. Interlaminar shear stresses, i.e., antiplane stresses, are shown to be present at the interfaces, especially near material discontinuities where gradients of in-plane stresses are usually high. For illustrating its practical application, the problem of a plate containing a hole patched with an intact plate is solved.

Terramechanics-based wheel–terrain interaction model and its applications to off-road wheeled mobile robots

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 491-503 ◽  
Author(s):  
Zhenzhong Jia ◽  
William Smith ◽  
Huei Peng
Keyword(s):  
Mobile Robots ◽  
Soft Soil ◽  
Three Dimensional ◽  
Interaction Model ◽  
Dynamics Simulation ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Wheeled Mobile Robots ◽  
Modular Model ◽  
Reaction Forces

SUMMARYThis paper presents a wheel–terrain interaction model, which enables efficient modeling of wheeled locomotion in soft soil and numerical simulations of off-road mobile robots. This modular model is derived based on wheel kinematics and terramechanics and the main focus is on describing the stress distributions along the wheel–terrain interface and the reaction forces exerted on the wheel by the soil. When the wheels are steered, the shear stresses underneath the wheel were modeled based on isotropic assumptions. The forces and torques contributed by the bulldozing effect of the side surfaces is also considered in the proposed model. Furthermore, the influence of grousers, commonly used on smaller mobile robots, was modeled by (1) averaging the normal pressures contributed by the grousers and the wheel concave portion, and (2) assuming that the shear phenomenon takes places along the grouser tips. By integrating the model with multibody system code for vehicle dynamics, simulation studies of various off-road conditions in three-dimensional environments can be conducted. The model was verified by using field experiment data, both for a single-wheel vehicle and a whole vehicle.

The Interlaminar Stresses Analysis of Composite Laminated Plates Based on the Generalized Higher-Order Global-Local Plate Theory

2013 ◽  
Vol 785-786 ◽  
pp. 239-243
Author(s):  
Wei Dong Chen ◽  
Ping Jia ◽  
Jian Cao Li ◽  
Feng Chao Zhang ◽  
Yan Chun Yu ◽  
...  
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Higher Order ◽  
Fortran Program ◽  
Laminated Plates ◽  
Local Theory ◽  
Shear Stresses ◽  
Interlaminar Stresses ◽  
Integration Problem ◽  
Triangular Area

A generalized higher-order global-local theory was presented. The transverse shear stresses can be got directly through the constitutive equation without using the equilibrium equation. The second derivative of interpolation function was deduced. The hammer integration of triangular area coordinate method was applied to solve the multiple integration problem of the element stiffness matrix. The order choice of numerical integration was discussed and results obtained through two different integration orders were compared. The flow of how to compile a FORTRAN program was given. A moderately thick composite laminated plate was analyzed via finite element method (FEM) based on the theory and results were compared with that of Paganos three-dimensional elasticity. It shows that the interlaminar stresses are accurate for moderately thick laminated plates.

scholarly journals A simple higher-order beam model that is represented by two kinematic variables and three section constants

2021 ◽  
pp. 108128652098887
Author(s):  
Hart Honickman ◽  
Stefan Kloppenborg
Keyword(s):  
Infinite Series ◽  
Transverse Shear ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Shear Stiffness ◽  
Higher Order ◽  
Shear Stresses ◽  
Beam Model ◽  
Stress Distributions ◽  
Transverse Shear Stresses

This article presents a new higher-order beam model. The present beam model is governed by differential equations that are similar to those present in some existing higher-order beam models; however, the present beam model makes use of a novel method of calculating the transverse shear stiffness, which facilitates the calculation of a shear-warping stiffness without the need for an assumed warping displacement field, and without introducing any additional kinematic variables. The present beam model also facilitates the recovery of the distributions of longitudinal normal stresses and transverse shear stresses. The authors postulate that the bending and shear terms in first-order shear deformation theory represent the first two terms in an infinite series that would constitute an ideal one-dimensional beam model, and it is suggested that the present beam model constitutes the first four terms in this hypothetical infinite series. The present beam model is solved for several example beams, and the results are compared with those of existing classical and higher-order beam models, as well as computational results from finite element analyses. It is shown that the present beam model is able to accurately represent deformed shapes and stress distributions pertaining to beams that exhibit non-trivial shear compliance as well as non-trivial shear-warping stiffness. In the case of laminated composite beams comprising a large number of laminae, the present beam model offers a level of analytical fidelity that is comparable to that of existing zigzag beam models; however, unlike zigzag beam models, the present beam model is equally well suited for the analyses of beams comprising any number of laminae.

Finite Element Analysis of Tire/Rim Interface Forces Under Braking and Cornering Loads

1992 ◽  
Vol 20 (2) ◽  
pp. 83-105 ◽  
Author(s):  
J. P. Jeusette ◽  
M. Theves
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Contact Pressure ◽  
Element Model ◽  
Shear Stresses ◽  
Detailed Knowledge ◽  
Stress Distributions ◽  
Element Analysis ◽  
Plane Shear ◽  
Normal Contact

Abstract During vehicle braking and cornering, the tire's footprint region may see high normal contact pressures and in-plane shear stresses. The corresponding resultant forces and moments are transferred to the wheel. The optimal design of the tire bead area and the wheel requires a detailed knowledge of the contact pressure and shear stress distributions at the tire/rim interface. In this study, the forces and moments obtained from the simulation of a vehicle in stationary braking/cornering conditions are applied to a quasi-static braking/cornering tire finite element model. Detailed contact pressure and shear stress distributions at the tire/rim interface are computed for heavy braking and cornering maneuvers.

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