Axisymmetric Thin Shell Analyses With Reduced Degrees-of-Freedom

1989 ◽  
Vol 42 (11S) ◽  
pp. S3-S12 ◽  
Author(s):  
C. A. Almeida ◽  
F. M. N. de Souza
Keyword(s):  
Displacement Field ◽  
Thin Shell ◽  
Degrees Of Freedom ◽  
Element Formulation ◽  
Shear Deformations ◽  
Bending Strain ◽  
Strain Components ◽  
Independent Degree ◽  
Displacement Based ◽  
Interpolation Functions

The formulation of a simple but effective unidimensional isoparametric displacement-based thin axisymmetric element is presented. The geometry is approximated by using cubic interpolation functions along the shell midsurface generatrix line and the element displacement field is represented by two spatial translation degrees-of-freedom only. The element kinematics incorporates membrane and bending strain components with the assumption of zero transverse shear deformations in the longitudinal and circumferential directions of the shell. This condition allows formulation of the element without using rotation as an independent degree-of-freedom, but continuity conditions between elements should be properly accounted for. The interaction effects between two adjoining elements or between an element and a rigid flange are modeled by using a penalty procedure to enforce continuity on the derivatives in the element midsurface radial displacements. The element formulation has been implemented and the results of various sample analyses are given to illustrate its effectiveness.

A new approach to curvature measures in linear shell theories

2020 ◽  
pp. 108128652097275
Author(s):  
Miroslav Šilhavý
Keyword(s):  
Strain Tensor ◽  
Middle Surface ◽  
Surface Strain ◽  
Affine Function ◽  
Shear Deformations ◽  
Strain Measure ◽  
Bending Strain ◽  
Curvature Measures ◽  
Tensor Formula ◽  
Strain Measures

The paper presents a coordinate-free analysis of deformation measures for shells modeled as 2D surfaces. These measures are represented by second-order tensors. As is well-known, two types are needed in general: the surface strain measure (deformations in tangential directions), and the bending strain measure (warping). Our approach first determines the 3D strain tensor E of a shear deformation of a 3D shell-like body and then linearizes E in two smallness parameters: the displacement and the distance of a point from the middle surface. The linearized expression is an affine function of the signed distance from the middle surface: the absolute term is the surface strain measure and the coefficient of the linear term is the bending strain measure. The main result of the paper determines these two tensors explicitly for general shear deformations and for the subcase of Kirchhoff-Love deformations. The derived surface strain measures are the classical ones: Naghdi’s surface strain measure generally and its well-known particular case for the Kirchhoff-Love deformations. With the bending strain measures comes a surprise: they are different from the traditional ones. For shear deformations our analysis provides a new tensor [Formula: see text], which is different from the widely used Naghdi’s bending strain tensor [Formula: see text]. In the particular case of Kirchhoff–Love deformations, the tensor [Formula: see text] reduces to a tensor [Formula: see text] introduced earlier by Anicic and Léger (Formulation bidimensionnelle exacte du modéle de coque 3D de Kirchhoff–Love. C R Acad Sci Paris I 1999; 329: 741–746). Again, [Formula: see text] is different from Koiter’s bending strain tensor [Formula: see text] (frequently used in this context). AMS 2010 classification: 74B99

The DDA Method

2016 ◽  
pp. 90-102
Author(s):  
Katalin Bagi
Keyword(s):  
Numerical Integration ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Short Overview ◽  
Abrupt Changes ◽  
Discontinuous Deformation ◽  
Iteration Technique

“DDA” stands for “Discontinuous Deformation Analysis”, suggesting that the displacement field of the analyzed domain shows abrupt changes on the element boundaries in the model. This chapter introduces the theoretical fundaments of DDA: mechanical characteristics of the elements together with the basic degrees of freedom, contact behavior, the equations of motion and their numerical integration with the help of Newmark's beta-method taking into account contact creation, loss and sliding with the help of an open-close iteration technique. Finally, a short overview on practical and scientific applications for masonry structures is given.

A Local Refinement Technique for B-Spline Finite Element Shell Modeling

2013 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Finite Element ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Element Model ◽  
Complex Structures ◽  
Local Refinement ◽  
B Spline ◽  
Spline Finite Element ◽  
Shell Finite Element

This paper presents a refinement technique for a B2-spline degenerate isoparametric shell finite element model for the analysis of the vibrational behavior of thin and moderately thick-walled structures. Complex structures to be refined are modeled by means of FE B-spline patches assembled with C0 continuity as usual in FE technique. The model refinement was performed by adding, on the domain of the selected patch, a tensorial set of polynomial B-spline functions, defined on local clamped knot vectors, and normalizing all the functions so that the resulting displacement field remain polynomial and continuous overall the domain except on the boundaries of the refined subdomain. A degrees of freedom trasformation, based on the knot-insertion algorthim, is adopted in order to guarantee the C0 continuity of the displacement field on the boundaries of the refined subdomain. Two numerical examples are presented in order to test the proposed approach. The natural frequencies of two structures, computed by means of the proposed modelling technique, are compared with reference results available in the literature or computed by means of reference standard FE models. Strengths and limits of the approach are finally discussed.

scholarly journals Generalized finite element formulation for efficient first-order plastic hinge analysis

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983636
Author(s):  
Dae-Jin Kim ◽  
Hong-Jun Son ◽  
Yousun Yi ◽  
Sung-Gul Hong
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Plastic Hinge ◽  
Computational Cost ◽  
Finite Element Formulation ◽  
Solution Technique ◽  
Element Formulation ◽  
Plastic Hinges ◽  
First Order ◽  
Generalized Finite Element

This article presents generalized finite element formulation for plastic hinge modeling based on lumped plasticity in the classical Euler–Bernoulli beam. In this approach, the plastic hinges are modeled using a special enrichment function, which can describe the weak discontinuity of the solution at the location of the plastic hinge. Furthermore, it is also possible to insert a plastic hinge at an arbitrary location of the element without modifying its connectivity or adding more elements. Instead, the formations of the plastic hinges are achieved by hierarchically adding more degrees of freedom to existing elements. Due to these features, the proposed methodology can efficiently perform the first-order plastic hinge analysis of large-frame structures. A generalized finite element solution technique based on the static condensation scheme is also proposed in order to reduce the computational cost of a series of linear elastic problems, which is in general the most time-consuming portion of the first-order plastic hinge analysis. The effectiveness and accuracy of the proposed method are verified by analyzing several representative numerical examples.

Asynchronous seismic analysis of concrete-faced rockfill dams including dam–reservoir interaction

2005 ◽  
Vol 32 (5) ◽  
pp. 940-947 ◽  
Author(s):  
Alemdar Bayraktar ◽  
Kemal Haciefendioglu ◽  
Murat Muvafik
Keyword(s):  
Finite Element ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Coupled System ◽  
Lagrangian Approach ◽  
Element Formulation ◽  
Dam Reservoir ◽  
Torul Dam ◽  
Displacement Based ◽  
Isoparametric Finite Elements

Seismic response of concrete-faced rockfill (CFR) dams subjected to asynchronous base excitation is determined by considering dam–reservoir interaction. The equations of motion of the coupled system are obtained using the Lagrangian approach, and the surface sloshing motion is included in the finite element formulation. Torul dam constructed in the city, Gumushane, Turkey, is selected as a numerical example, and its material properties are considered in the analysis. The dam–reservoir interaction system is modelled using the Lagrangian (displacement-based) fluid and solid-quadrilateral-isoparametric finite elements. The east–west component of Erzincan earthquake, which occurred on 13 March 1992, recorded near the region of the dam is used as a ground motion. Propagation velocities of the seismic wave are chosen as 1000 m/s, 3000 m/s, and infinite. Stresses are calculated for empty and full reservoir cases and compared with each other.Key words: concrete-faced rockfill dam, Lagrangian approach, dam–reservoir interaction, finite element method, earthquake.

Continuum Modeling of a Slewing ISAT (Innovative Space Antenna Technology)

2005 ◽  
Author(s):  
Armaghan Salehian ◽  
Eugene M. Cliff ◽  
Daniel J. Inman
Keyword(s):  
Continuum Model ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Space Antenna ◽  
Geometrical Properties ◽  
Strain Components ◽  
Equivalent Continuum Model ◽  
Equivalent Continuum ◽  
Very High ◽  
The Continuum

A simple approach is presented herein for obtaining the equivalent continuum model of an ISAT (Innovative Space Antenna Technology) truss structure in order to find the free vibration solutions for different coordinates of vibration. Kinetic and potential energy expressions are written in terms of the strain components of the elements and the nodal velocities. The Lagrangian approach is employed to find the governing partial differential equations of the structure which for the bending degrees of freedom lead to an equivalent Timoshenko beam. Finally, the physical characteristics of the continuum model are written in terms of the material and geometrical properties of the truss, which provide a simple tool for comparing dynamic characteristics of lattices with different properties. The natural frequencies are found for each of the bending, longitudinal, and torsional coordinates of vibration and are compared to those of a FEM solution for the purpose of validation. The analytical model shows very high accuracy in prediction of the natural frequencies of the original truss.

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