scholarly journals Free and Forced Vibration of Laminated and Sandwich Plates by Zig-Zag Theories Differently Accounting for Transverse Shear and Normal Deformability

Aerospace ◽  
2018 ◽  
Vol 5 (4) ◽  
pp. 108 ◽  
Author(s):  
Ugo Icardi ◽  
Andrea Urraci
Keyword(s):  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Interfacial Stress ◽  
Sandwich Plates ◽  
Displacement Fields ◽  
Element Analysis ◽  
Out Of Plane ◽  
Elasticity Solutions ◽  
Displacement Based

A number of mixed and displacement-based zig-zag theories are derived from the zig-zag adaptive theory (ZZA). As a consequence of their different assumptions on displacement, strain, and stress fields, and layerwise functions, these theories account for the transverse shear and normal deformability in different ways, but their unknowns are independent of the number of layers. Some have features that are reminiscent of ones that have been published in the literature for the sake of comparison. Benchmarks with different length-to-thickness ratios, lay-ups, material properties, and simply supported or clamped edges are studied with the intended aim of contributing toward better understanding the influence of transverse anisotropy on free vibration and the response of blast-loaded, multilayered, and sandwich plates, as well as enhancing the existing database. The results show that only theories whose layerwise contributions identically satisfy interfacial stress constrains and whose displacement fields are redefined for each layer provide results that are in agreement with elasticity solutions and three-dimensional (3D) finite element analysis (FEA) (mixed solid elements with displacements and out-of-plane stresses as nodal degrees of freedom (d.o.f.)) with a low expansion order of polynomials in the in-plane and out-of-plane directions. The choice of their layerwise functions is shown to be immaterial, while theories with fixed kinematics are shown to be strongly case-sensitive and often inadequate (even for slender components).

Three-dimensional vibration of a ring with a noncircular cross-section on an elastic foundation

2017 ◽  
Vol 232 (13) ◽  
pp. 2381-2393 ◽  
Author(s):  
Zhe Liu ◽  
Fuqiang Zhou ◽  
Christian Oertel ◽  
Yintao Wei
Keyword(s):  
Elastic Foundation ◽  
Cross Section ◽  
Three Dimensional ◽  
Theoretical Formula ◽  
Variation Principle ◽  
Displacement Fields ◽  
Element Analysis ◽  
Noncircular Cross Section ◽  
Truck Tire ◽  
Out Of Plane

The three-dimensional dynamic equations of a ring with a noncircular cross-section on an elastic foundation are obtained using the Hamilton variation principle. In contrast to the previous rings on elastic foundation model, the developed model incorporates both the in-plane and out-of-plane bend and the out-of-plane torsion in displacement fields. The errors in the derivation of the initial stress and the work of the internal pressure in previous rings on elastic foundation models have been corrected. The mode expansion was used to obtain the analytical solution of the natural frequency. The initial motivation is to develop a theoretical model for car tire dynamics. Therefore, to validate the proposed model, the in-plane and out-of-plane vibrations of a truck tire have been analyzed using the proposed method. To further verify the accuracy of the model, the results of the theoretical formula are compared with the finite element analysis and modal test, and good agreement can be found.

scholarly journals Isogeometric Implementation of High-Order Microplane Model for the Simulation of High-Order Elasticity, Softening, and Localization

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Erol Lale ◽  
Xinwei Zhou ◽  
Gianluca Cusatis
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Control Point ◽  
Three Dimensional ◽  
Local Strain ◽  
High Order ◽  
Particle Model ◽  
Displacement Fields ◽  
Displacement Based ◽  
The Continuum

In this paper, a recently developed higher-order microplane (HOM) model for softening and localization is implemented within a isogeometric finite-element framework. The HOM model was derived directly from a three-dimensional discrete particle model, and it was shown to be associated with a high-order continuum characterized by independent rotation and displacement fields. Furthermore, the HOM model possesses two characteristic lengths: the first associated with the spacing of flaws in the material internal structure and related to the gradient character of the continuum; the second associated with the size of these flaws and related to the micropolar character of the continuum. The displacement-based finite element implementation of this type of continua requires C1 continuity both within the elements and at the element boundaries. This motivated the implementation of the concept of isogeometric analysis which ensures a higher degree of smoothness and continuity. Nonuniform rational B-splines (NURBS) based isogeometric elements are implemented in a 3D setting, with both displacement and rotational degrees-of-freedom at each control point. The performed numerical analyses demonstrate the effectiveness of the proposed HOM model implementation to ensure optimal convergence in both elastic and softening regime. Furthermore, the proposed approach allows the natural formulation of a localization limiter able to prevent strain localization and spurious mesh sensitivity known to be pathological issues for typical local strain-softening constitutive equations.

Influence of Interference and Clamping on Fretting Fatigue in Single Rivet-Row Lap Joints

2000 ◽  
Vol 123 (4) ◽  
pp. 686-698 ◽  
Author(s):  
K. Iyer ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Crack Initiation ◽  
Three Dimensional ◽  
Fretting Fatigue ◽  
Cyclic Stress ◽  
Lap Joints ◽  
Element Analysis ◽  
Out Of Plane ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Fretting Damage

Primary fretting fatigue variables such as contact pressure, slip amplitude and bulk cyclic stresses, at and near the contact interface between the rivet shank and panel hole in a single rivet-row, 7075-T6 aluminum alloy lap joint are presented. Three-dimensional finite element analysis is applied to evaluate these and the effects of interference and clamping stresses on the values of the primary variables and other overall measures of fretting damage. Two rivet geometries, non-countersunk and countersunk, are considered. Comparison with previous evaluations of the fretting conditions in similar but two-dimensional connections indicates that out-of-plane movements and attending effects can have a significant impact on the fatigue life of riveted connections. Variations of the cyclic stress range and other proponents of crack initiation are found to peak at distinct locations along the hole-shank interface, making it possible to predict crack initiation locations and design for extended life.

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.

An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
M. Jafari ◽  
M. J. Mahjoob
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Direct Method ◽  
Three Dimensional ◽  
Curved Beams ◽  
Element Analysis ◽  
Shear Loads ◽  
Line Passing ◽  
Exact Stiffness Matrix

In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

Numerical Optimization of Silicon Stacked Module for 3-D Packaging Applications

2008 ◽  
Vol 5 (2) ◽  
pp. 68-76
Author(s):  
Akella G.K. Viswanath ◽  
Xiaowu Zhang ◽  
Y.Y. Wang ◽  
S.W. Yoon ◽  
Navas Khan ◽  
...  
Keyword(s):  
Solder Joint ◽  
Functional Integration ◽  
Three Dimensional ◽  
Interfacial Stress ◽  
Electrical Performance ◽  
Thickness Variation ◽  
Element Analysis ◽  
Variation Of Parameters ◽  
Optimization Study ◽  
Electroplated Copper

Three-dimensional package format has gained more popularity for various applications because of the trend toward higher functional integration, miniaturization, and better electrical performance. This paper presents a design optimization study of a 3-D package using a silicon interposer. The package consists of three stacks with five dies. Electrical connections through the silicon interposers are done by through-silicone vias (TSVs) filled with electroplated copper. Initially, structural optimization of the package is conducted by a 2-D finite element analysis and later, statistical analysis is performed to estimate the coupled effects of parameters considered for the design. Carrier thickness variation is found to be the most significant effect on the package warpage. Interfacial stress between the copper plug and the silicon via hole has been investigated and reported. A 3-D model is constructed for the solder joint reliability study with SnAgCu material properties. Solder joint life with variation of parameters (i.e., board level underfill, higher standoff solder interconnect, and low CTE board) is studied, and all results are reported accordingly.

Analysis of Three-Dimensional Clamped Single Edge Notched Tension (SENT) Specimens

2018 ◽  
Author(s):  
Zheng Liu ◽  
Xu Chen ◽  
Xin Wang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Depth ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Width Ratio ◽  
Element Analysis ◽  
Out Of Plane ◽  
T Stress

In the present paper, three-dimensional clamped SENT specimens, which is one of the most widely used low-constraint and less-conservative specimen, are analyzed by using a crack compliance analysis approach and extensive finite element analysis. Considering the test standard (BS8571) recommended specimen sizes, the daylight to width ratio, H/W, is 10.0, the relative crack depth, a/W, is varied by 0.2, 0.3, 0.4, 0.5 or 0.6 and the relative plate thickness, B/W, is chosen by 1.0, 2.0 or 4.0, respectively. Complete solutions of fracture mechanics parameters, including stress intensity factor (K), in-plane T-stress (T11) and out-of-plane T-stress (T33) are calculated, and the results obtained from above two methods have a good agreement. Moreover, the combination of the effects of a/W and B/W on the stress intensity factor K, T11 and T33 stress are thus illustrated.

scholarly journals Nonlinear Mechanics of Beams With Partial Piezoelectric Layers

2019 ◽  
Vol 86 (10) ◽  
Author(s):  
Hamed Farokhi ◽  
Mergen H. Ghayesh
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Coupled Model ◽  
Beam Theory ◽  
Internal Resonances ◽  
Element Analysis ◽  
Nonlinear Dynamical ◽  
Dimensional Finite Element ◽  
Resonant Region ◽  
Three Dimensional Finite Element

Abstract This paper investigates the nonlinear static response as well as nonlinear forced dynamics of a clamped–clamped beam actuated by piezoelectric patches partially covering the beam from both sides. This study is the first to develop a high-dimensional nonlinear model for such a piezoelectric-beam configuration. The nonlinear dynamical resonance characteristics of the electromechanical system are examined under simultaneous DC and AC piezoelectric actuations, while highlighting the effects of modal energy transfer and internal resonances. A multiphysics coupled model of the beam-piezoelectric system is proposed based on the nonlinear beam theory of Bernoulli–Euler and the piezoelectric constitutive equations. The discretized model of the system is obtained with the help of the Galerkin weighted residual technique while retaining 32 degrees-of-freedom. Three-dimensional finite element analysis is conducted as well in the static regime to validate the developed model and numerical simulation. It is shown that the response of the system in the nonlinear resonant region is strongly affected by a three-to-one internal resonance.

Electronic Speckle Pattern Interferometry Applied to the Displacement Measurement of Sandwich Plates with Single ‘Fully Potted’ Insert

2004 ◽  
Vol 20 (4) ◽  
pp. 273-276 ◽  
Author(s):  
S. J. Huang ◽  
H. L. Lin
Keyword(s):  
Speckle Pattern ◽  
Fem Analysis ◽  
Electronic Speckle Pattern Interferometry ◽  
Sandwich Plates ◽  
Destructive Testing ◽  
Displacement Fields ◽  
Full Field ◽  
Out Of Plane ◽  
Plane Displacement ◽  
Non Destructive

AbstractThe construction and operation of electronic speckle pattern interferometer (ESPI) applied to single-inserted sandwich plates have been earliest presented in this paper. Proposed ESPI has advantages of full-field and non-destructive testing, which can measures microscopic out-of-plane displacement in the elastic region without wasting specimen. For validation purpose, the finite element method (FEM) analysis was conducted. By comparing the results of ESPI and FEM displacement fields around the inserts that a convincing agreement is revealed. The effect of potting material diameter on the displacement of single-inserted sandwich plates was obtained by the ESPI and FEM.

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