Geometrically exact hybrid beam element based on nonlinear programming

This work presents a hybrid shear‐flexible beam‐element, capable of capturing arbitrarily large inelastic displacements and rotations of planar frame structures with just one element per member. Following Reissner's geometrically exact theory, the finite element problem is herein formulated wit...

Full description

Saved in:
Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 122; no. 13; pp. 3273 - 3299
Main Authors: Lyritsakis, Charilaos M., Andriotis, Charalampos P., Papakonstantinou, Konstantinos G.
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 15.07.2021
Wiley Subscription Services, Inc
Subjects:
Beams (structural)
Centroids
Displacement
Exact solutions
fiber cross‐sections
Finite element method
Frame structures
geometrically exact element
hybrid beam element
Lagrange multiplier
Locking
material nonlinearities
Nonlinear programming
Numerical integration
Optimization
Potential energy
Quadratures
Quadrilaterals
shear deformations
Strain
ISSN:0029-5981, 1097-0207
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This work presents a hybrid shear‐flexible beam‐element, capable of capturing arbitrarily large inelastic displacements and rotations of planar frame structures with just one element per member. Following Reissner's geometrically exact theory, the finite element problem is herein formulated within nonlinear programming principles, where the total potential energy is treated as the objective function and the exact strain‐displacement relations are imposed as kinematic constraints. The approximation of integral expressions is conducted by an appropriate quadrature, and by introducing Lagrange multipliers, the Lagrangian of the minimization program is formed and solutions are sought based on the satisfaction of necessary optimality conditions. In addition to displacement degrees of freedom at the two element edge nodes, strain measures of the centroid act as unknown variables at the quadrature points, while only the curvature field is interpolated, to enforce compatibility throughout the element. Inelastic calculations are carried out by numerical integration of the material stress‐strain law at the cross‐section level. The locking‐free behavior of the element is presented and discussed, and its overall performance is demonstrated on a set of well‐known numerical examples. Results are compared with analytical solutions, where available, and outcomes based on flexibility‐based beam elements and quadrilateral elements, verifying the efficiency of the formulation.
Bibliography:Funding information
Division of Civil, Mechanical and Manufacturing Innovation, 1634575
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6663