scholarly journals ON EVALUATION OF THE THREE-DIMENSIONAL ISOGEOMETRIC BEAM ELEMENT

2020 ◽  
Vol 26 ◽  
pp. 24-29
Author(s):  
Edita Dvořáková ◽  
Bořek Patzák
Keyword(s):  
Three Dimensional ◽  
Beam Element ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Computational Domain ◽  
Conic Sections ◽  
Geometrically Nonlinear Analysis ◽  
Straight Beam ◽  
Approximation Errors ◽  
Standard Finite Element Method

The exact description of the arbitrarily curved geometries, including conic sections, is an undeniable advantage of isogeometric analysis (IGA) over standard finite element method (FEM). With B-spline/NURBS approximation functions used for both geometry and unknown approximations, IGA is able to exactly describe beams of various shapes and thus eliminate the geometry approximation errors. Moreover, naturally higher continuity than standard C0 can be provided along the entire computational domain. This paper evaluates the performance of the nonlinear spatial Bernoulli beam adapted from formulation of Bauer et al. [1]. The element formulation is presented and the comparison with standard FEM straight beam element and fully three-dimensional analysis is provided. Although the element is capable of geometrically nonlinear analysis, only geometrically linear cases are evaluated for the purposes of this study.

A CO-ROTATIONAL FORMULATION FOR GEOMETRICALLY NONLINEAR FINITE ELEMENT ANALYSIS OF SPATIAL BEAMS

1994 ◽  
Vol 18 (1) ◽  
pp. 65-88 ◽  
Author(s):  
L. Jiang ◽  
M.W. Chernuka
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Internal Force ◽  
Beam Element ◽  
Geometrically Nonlinear ◽  
Element Analysis ◽  
Finite Element Program ◽  
Geometrically Nonlinear Analysis ◽  
Spatial Beams

A co-rotational procedure is presented in this paper for handling arbitrarily large three-dimensional rotations associated with geometrically nonlinear analysis of spatial beam structures. This procedure has been incorporated into two commonly used 3-D beam elements, the 2-node cubic beam element and the 3-node superparametric beam element, in our in-house general purpose finite element program, VAST. In the present procedure, the element tangent stiffness matrices are generated by using the standard updated Lagrangian formulation, while a co-rotational formulation is employed to update the internal force vectors during the Newton-Raphson iterations, A number of example problems have been analyzed and the result are in good agreement with analytical or published numerical solutions.

A Three-Dimensional Geometrically Nonlinear Analysis of Pipelaying in an Ocean Environment

1981 ◽  
Vol 103 (2) ◽  
pp. 201-205
Author(s):  
S. Odorizzi ◽  
B. A. Schrefler
Keyword(s):  
Hydrostatic Pressure ◽  
Nonlinear Analysis ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Bending Stiffness ◽  
Ocean Floor ◽  
Geometrically Nonlinear ◽  
External Hydrostatic Pressure ◽  
Geometrically Nonlinear Analysis ◽  
Ocean Environment

A three-dimensional analysis for pipelines suspended between the ocean floor and a laying barge or a stinger is presented. The analysis performed is capable of handling not only variations in bending stiffness, weight and buoyancy, crosscurrents and lateral bay drift, but also the effects of external hydrostatic pressure and buckling of the pipes. For this purpose a total Lagrangian geometrically nonlinear analysis in space. Examples are given which demonstrate the versatility of the analysis proposed.

Element-Independent Pure Deformational and Co-Rotational Methods for Triangular Shell Elements in Geometrically Nonlinear Analysis

2018 ◽  
Vol 18 (05) ◽  
pp. 1850065 ◽  
Author(s):  
Y. Q. Tang ◽  
Y. P. Liu ◽  
S. L. Chan
Keyword(s):  
Nonlinear Analysis ◽  
Nonlinear Problems ◽  
Shell Element ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Plate Element ◽  
Membrane Element ◽  
Geometrically Nonlinear Analysis ◽  
Shell Elements

Proposed herein is a novel pure deformational method for triangular shell elements that can decrease the element quantities and simplify the element formulation. This approach has computational advantages over the conventional finite element method for linear and nonlinear problems. In the element level, this method saves time for computing stresses, internal forces and stiffness matrices. A flat shell element is formed by a membrane element and a plate element, so that the pure deformational membrane and plate elements are derived and discussed separately in this paper. Also, it is very convenient to incorporate the proposed pure deformational method into the element-independent co-rotational (EICR) framework for geometrically nonlinear analysis. Thus, on the basis of the pure deformational method, a novel EICR formulation is proposed which is simpler and has more clear physical characteristics than the traditional formulation. In addition, a triangular membrane element with drilling rotations and the discrete Kirchhoff triangular plate element are used to verify the proposed pure deformational method, although several benchmark problems are employed to verify the robustness and accuracy of the proposed EICR formulations.

Geometrically Nonlinear Analysis of Smart Sandwich Plates

2015 ◽  
Vol 813-814 ◽  
pp. 1085-1089
Author(s):  
B. Basa ◽  
S. Das ◽  
Saroj K. Sarangi
Keyword(s):  
Nonlinear Analysis ◽  
Fiber Composite ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Sandwich Plates ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Active Fiber ◽  
Active Fiber Composite

This paper presents the geometrically nonlinear analysis of smart sandwich plates. The top surface of the plate is integrated with a layer of commercially available active fiber composite. Considering the First order shear deformation theory individually for each layer of the sandwich plate, a three-dimensional finite element model has been developed. The performance of active fiber composite for the smart control of geometrically nonlinear deflection of the sandwich plates has been studied and numerical results are presented.

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