Sandwich Shell Finite Element for Dynamic Explicit Analysis

2000 ◽  
Author(s):  
Ala Tabiei ◽  
Romil Tanov ◽  
Victor Birman
Keyword(s):  
Finite Element ◽  
Transverse Shear ◽  
Critical Time ◽  
Shell Element ◽  
Shear Stresses ◽  
Sandwich Shell ◽  
Time Step ◽  
Third Order ◽  
Explicit Analysis ◽  
Sandwich Shells

Abstract This work presents the finite element (FE) formulation and implementation of a higher order shear deformable shell element for dynamic explicit analysis of composite and sandwich shells. The formulation is developed using a displacement based third order shear deformation shell theory. Using the differential equilibrium equations and the interlayer requirements, a treatment is developed for the transverse shear, resulting in a continuous, piecewise quartic distribution of the transverse shear stresses through the shell thickness. The FE implementation is cast into a 4-noded quadrilateral shell element with 9 degrees of freedom (DOF) per node. Only C0 continuity of the displacement functions is required in the shell plane, which makes the present formulation applicable to the most common 4-noded bilinear isoparametric shell elements. Expressions are developed for the critical time step of the explicit time integration for orthotropic homogeneous and layered shells based on the developed third order formulation. To assess the performance of the present shell element it is implemented in the general nonlinear explicit dynamic FE code DYNA3D. Several problems are solved and results are compared to other theoretical and numerical results. The developed sandwich shell element is much more computationally efficient for modeling sandwich shells than solid elements.

Bending Analysis of SMA Embedded Rectangular Laminated Sandwich Plates with Soft Core Using 3D Finite Element Method

2011 ◽  
Vol 110-116 ◽  
pp. 1458-1465 ◽  
Author(s):  
M. Khadem ◽  
M. M. Kheirikhah
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transverse Shear ◽  
Soft Core ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
3D Finite Element ◽  
Bending Analysis ◽  
Transverse Shear Stresses ◽  
3D Finite Element Method

Nowadays Shape Memory Alloys (SMAs) are used as actuators in many applications such as aerospace structures. In sandwich structures, the SMA wires or plates are used in the skins for shape control of the structure or vibration damping. In this paper, bending behavior of sandwich plates with embedded SMA wires in their skins is studied. 3D finite element method is used for construction and analysis of the sandwich plate with a flexible core and two stiff skins. Some important points such as continuity conditions of the displacements, satisfaction of interlaminar transverse shear stresses, the conditions of zero transverse shear stresses on the upper and lower surfaces and in-plane and transverse flexibility of soft core are considered for accurate modeling and analysis of sandwich structures. Solution for bending analysis of sandwich plates under various transverse loads are presented and the effect of many parameters such as plate dimensions, loading conditions, material properties of core, skins and SMA wires are studied. Comparison of the present results in special case with those of the three-dimensional theory of elasticity and some plate theories confirms the accuracy of the proposed model.

A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY

2012 ◽  
Vol 04 (01) ◽  
pp. 1250010 ◽  
Author(s):  
V. P. VALLALA ◽  
G. S. PAYETTE ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Beam Theory ◽  
Element Model ◽  
Higher Order ◽  
Time Step ◽  
Third Order ◽  
The Third

In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

scholarly journals Assessment of Susceptibility to Liquefaction of Saturated Road Embankment Subjected to Dynamic Loads

2014 ◽  
Vol 36 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Anna Borowiec ◽  
Krzysztof Maciejewski
Keyword(s):  
Factor Of Safety ◽  
Stress Component ◽  
Critical Time ◽  
Water Reservoir ◽  
Constitutive Relationship ◽  
Plastic Behavior ◽  
Shear Stresses ◽  
Time Step ◽  
The Road ◽  
Liquefaction Susceptibility

Abstract Liquefaction has always been intensely studied in parts of the world where earthquakes occur. However, the seismic activity is not the only possible cause of this phenomenon. It may in fact be triggered by some human activities, such as constructing and mining or by rail and road transport. In the paper a road embankment built across a shallow water reservoir is analyzed in terms of susceptibility to liquefaction. Two types of dynamic loadings are considered: first corresponding to an operation of a vibratory roller and second to an earthquake. In order to evaluate a susceptibility of soil to liquefaction, a factor of safety against triggering of liquefaction is used (FSTriggering). It is defined as a ratio of vertical effective stresses to the shear stresses both varying with time. For the structure considered both stresses are obtained using finite element method program, here Plaxis 2D. The plastic behavior of the cohesionless soils is modeled by means of Hardening Soil (HS) constitutive relationship, implemented in Plaxis software. As the stress tensor varies with time during dynamic excitation, the FSTriggering has to be calculated for some particular moment of time when liquefaction is most likely to occur. For the purposes of this paper it is named a critical time and established for reference point at which the pore pressures were traced in time. As a result a factor of safety distribution throughout embankment is generated. For the modeled structure, cyclic point loads (i.e., vibrating roller) present higher risk than earthquake of magnitude 5.4. Explanation why considered structure is less susceptible to earthquake than typical dam could lay in stabilizing and damping influence of water, acting here on both sides of the slope. Analogical procedure is applied to assess liquefaction susceptibility of the road embankment considered but under earthquake excitation. Only the higher water table is considered as it is the most unfavorable. Additionally the modified factor of safety is introduced, where the dynamic shear stress component is obtained at a time step when its magnitude is the highest - not necessarily at the same time step when the pore pressure reaches its peak (i.e., critical time). This procedure provides a greater margin of safety as the computed factors of safety are smaller. Method introduced in the paper presents a clear and easy way to locate liquefied zones and estimate liquefaction susceptibility of the subsoil - not only in the road embankment.

Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory

1978 ◽  
Vol 45 (2) ◽  
pp. 371-374 ◽  
Author(s):  
T. J. R. Hughes ◽  
W. K. Liu
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Transient Analysis ◽  
Critical Time ◽  
Unconditional Stability ◽  
Time Step ◽  
Explicit Finite Element ◽  
New Family ◽  
Critical Time Step ◽  
Analysis Stability

A stability analysis is carried out for a new family of implicit-explicit finite-element algorithms. The analysis shows that unconditional stability may be achieved for the implicit finite elements and that the critical time step of the explicit elements governs for the system.

An analytical contact model for finite element analysis of tube spinning process

2008 ◽  
Vol 222 (11) ◽  
pp. 1375-1385 ◽  
Author(s):  
H Lexian ◽  
B M Dariani
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Shell Element ◽  
Fe Analysis ◽  
Contact Forces ◽  
Contact Model ◽  
Integration Scheme ◽  
Time Step ◽  
Tube Spinning ◽  
Spinning Process

This work presents an analytical contact model for non-linear dynamic finite element (FE) analysis of the tube spinning process that is based on the Belytschko—Lin—Tsay shell element with an explicit time integration scheme. A brief description of the FE formulation of a first-order shear deformation shell element as well as internal forces calculation, nodal mass calculation, and prediction of stable time step are presented. An analytical contact model is developed for a general roller. Analytical equations of the roller surfaces, interpenetration, and unit vector normal to the contact surface are determined. Contact forces are approximated by a penalty method with a suitable estimation of the penalty coefficient. An explicit FE code, using the developed analytical contact model, is designed and its implementation algorithm is described in detail. The dome forming process of a seamless pressure vessel is simulated using this code, in which the contact analysis is performed robustly, which saves significant amounts of computer time. A steel alloy DIN 1.7225 seamless pressure vessel, which was formed by a hot-spinning process, is cut longitudinally and its profile is measured. A comparison between the longitudinal cross-section profiles calculated by FE analysis and that obtained from experiment shows a good agreement.

Nonlinear Finite-Element Method for Plates and Its Application to Dynamic Response of Reactor Fuel Subassemblies

1974 ◽  
Vol 96 (4) ◽  
pp. 251-257 ◽  
Author(s):  
T. Belytschko ◽  
A. H. Marchertas
Keyword(s):  
Finite Element ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Shell Element ◽  
Nonlinear Material ◽  
Time Step ◽  
Cross Sectional ◽  
Difference Formula ◽  
Lumped Masses

A finite-element procedure for transient analysis of plates and shells in three-dimensional space, and applicable to large displacements and nonlinear material properties, is described. This procedure employs a convected coordinate formulation enabling the use of simple strain-nodal displacement and nodal force-stress relations. The plate/shell element considers linear in-plane displacements and cubic transverse displacements. The orientation of lumped masses is described by unit vectors so that arbitrarily large rotations can be treated. Discretized equations of motion are integrated explicitly in time with a difference formula. Membrane artificial viscosity is utilized to stabilize occasional oscillations. The computational efficiency of the procedure is quite good: one element-time step takes 2 msec on an IBM 360/195 computer. Comparison of results with experimental data of impulsively loaded plates shows good agreement. The program was applied to a hexagonal fuel subassembly loaded internally. Various results are presented on its response and it is shown that, for that type of loading, two-dimensional cross-sectional models may be adequate.

Compressive Response of Thermoplastic Composites by Layered Shell Elements

1992 ◽  
Author(s):  
Hassan Mahfuz ◽  
Cynthia R. Ingram ◽  
Shaik Jeelani
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shell Element ◽  
Material Behavior ◽  
Thermoplastic Composites ◽  
Shear Stresses ◽  
Layered Shell ◽  
Element Analysis ◽  
Shell Elements ◽  
Compressive Response

Abstract Thick Laminates of thermoplastic Composites (APC-2) are modeled with isoparametric layered shell elements to predict the responses of the laminate at various temperatures under compressive loading. A large displacement finite element analysis is performed by considering the geometric non-linearities in the composite structure. Multiple load steps with linear material behavior are used to model the load-displacement characteristics found in a previous experimental study. A detailed description of the layered shell element along with its formulations is presented to highlight the limitations and scope of this element in composite structural analysis. Compressive response in respect of displacements, normal stresses, shear stresses and interlaminar shear stresses under three different temperatures is presented. Laminate response along its length as well as through the thickness is also presented to analyze and understand the failure mechanisms under such loading. Experimental data from a previous study are compared with the current result to validate the finite element analysis.

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