| 1. |
- Alhasawi, Anas, et al.
(author)
-
Co-rotational planar beam element with generalized elasto-plastic hinges
- 2017
-
In: Engineering structures. - : Elsevier. - 0141-0296 .- 1873-7323. ; 151, s. 188-205
-
Journal article (peer-reviewed)abstract
- Slender elements in framed structures may undergo large displacement and experience highly nonlinear behavior. This paper presents a two-node co-rotational flexible beam with generalized elasto-plastic hinges at the beam ends. A Condensation procedure is used to remove the internal degrees of freedom so that the formulation is easily incorporated with the standard co-rotational approach. A family of asymmetric and convex yield surfaces of super-elliptic shape is considered for the plastic behavior of the hinges. By varying the roundness factor, an infinite number of yield surfaces are obtained making it possible to select the yield function that best fit experimental data of any type of cross-section and material. The nonlinear response of bolted connections subjected to both bending and axial forces are conveniently modeled with such a yield surface. Discrete constitutive equations for the hinge plastic deformations are derived using the implicit scheme for both smooth and non-smooth cases. Numerical examples demonstrate the accuracy of the model in predicting the large displacement inelastic response of framed structures. Effect of the roundness factor on the ultimate load strongly depends on the structure typology. It was observed that cyclic loading produces pinching effect, cyclic softening and ductile behavior. Those effects are more pronounced with anisotropic yield criteria.
|
|
| 2. |
- Alsafadie, Rabe, et al.
(author)
-
A comparative study of displacement and mixed-based corotational finite element formulations for elasto-plastic three-dimensional beam analysis
- 2011
-
In: Engineering computations. - : Emerald. - 0264-4401 .- 1758-7077. ; 28:7, s. 939-982
-
Journal article (peer-reviewed)abstract
- The purpose of this paper is to present eight local elasto-plastic beam element formulations incorporated into the corotational framework for two-noded three-dimensional beams. These formulations capture the warping torsional effects of open cross-sections and are suitable for the analysis of the nonlinear buckling and post-buckling of thin-walled frames with generic cross-sections. The paper highlights the similarities and discrepancies between the different local element formulations. The primary goal of this study is to compare all the local element formulations in terms of accuracy, efficiency and CPU-running time.
|
|
| 3. |
- Alsafadie, Rabe, et al.
(author)
-
Corotational mixed three-dimensional finite element for structural stability problems
- 2010
-
In: ECCM 2010, IV European Conference on Computational Mechanics.
-
Conference paper (peer-reviewed)abstract
- The corotational technique exploits the technology that applies to a two–noded element a coordinatesystem which continuously translates and rotates with the element. In this way, the rigid bodymotion is separated out from the deformational motion. In this paper, a mixed formulation is adoptedfor the derivation of the local element tangent stiffness matrix and nodal forces. The mixed finiteelement formulation is based on the two–field Hellinger–Reissner variational principle. This localelement, together with the corotational framework, can be used to analyze the nonlinear bucklingand postbuckling of thin–walled beams with arbitrary cross–section. The mixed formulation solutionis compared against the results obtained from a corotational displacement–based formulation havingthe same beam kinematics. The superiority of the mixed formulation is clearly demonstrated.
|
|
| 4. |
- Alsafadie, Rabe, et al.
(author)
-
Efficient local formulation for elasto-plastic corotational thin-walled beams
- 2011
-
In: The International Journal for Numerical Methods in Biomedical Engineering. - : Wiley. - 2040-7939. ; 27:4, s. 498-509
-
Journal article (peer-reviewed)abstract
- A local elasto-plastic formulation, based on a low-order nonlinear strain expression using Bernoulli beam kinematics, is presented in this paper. This element, together with the corotational framework proposed in (Comput. Meth. Appl. Mech. Eng. 2002; 191(17): 1755-1789) can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with arbitrary cross-section. The formulation captures both the Saint-Venant and warping torsional effects of open cross-sections. Numerical examples show that this local formulation is more efficient than the one proposed in (Comput. Meth. Appl. Mech. Eng. 2002; 191(51):5811-5831) based on a Timoshenko beam assumption.
|
|
| 5. |
- Alsafadie, Rabe, et al.
(author)
-
Stability analysis for 3D frames using mixed corotational formulation
- 2010
-
In: SDSS-Rio 2010 Stability and ductility of steel structures. ; , s. 547-554
-
Conference paper (peer-reviewed)abstract
- The corotational technique is adopted for the analysis of 3D beams. The technique applies to atwo-noded element a coordinate system which continuously translates and rotates with the element. Inthis way, the rigid body motion is separated out from the deformational motion. Then, a mixedformulation is adopted for the derivation of the local element tangent stiffness matrix and nodal forces.The mixed finite element formulation is based on an incremental form of the two-field Hellinger-Reissnervariational principle to permit elasto-plastic material behavior. The proposed element can be used toanalyze the nonlinear buckling and postbuckling of 3D beams. The mixed formulation solution iscompared against the results obtained from a corotational displacement-based formulation having thesame beam kinematics. The superiority of the mixed formulation is clearly demonstrated.
|
|
| 6. |
|
|
| 7. |
|
|
| 8. |
|
|
| 9. |
- Chhang, Sophy, 1988-
(author)
-
Energy-momentum conserving time-stepping algorithms for nonlinear dynamics of planar and spatial Euler-Bernoulli/Timoshenko beams
- 2018
-
Doctoral thesis (other academic/artistic)abstract
- Large deformations of flexible beams can be described using either the co-rotational approach or the total Lagrangian formalism. The co-rotational method is an attractive approach to derive highly nonlinear beam elements because it combines accuracy with numerical efficiency. On the other hand, the total Lagrangian formalism is the natural setting for the construction of geometrically exact beam theories. Classical time integration methods such as Newmark, standard midpoint rule or the trapezoidal rule do suffer severe shortcomings in nonlinear regimes. The construction of time integration schemes for highly nonlinear problems which conserve the total energy, the momentum and the angular momentum is addressed for planar co-rotational beams and for a geometrically exact spatial Euler-Bernoulli beam.In the first part of the thesis, energy-momentum conserving algorithms are designed for planar co-rotational beams. Both Euler-Bernoulli and Timoshenko kinematics are addressed. These formulations provide us with highly complex non-linear expressions for the internal energy as well as for the kinetic energy which involve second derivatives of the displacement field. The main idea of the algorithm is to circumvent the complexities of the geometric non-linearities by resorting to strain velocities to provide, by means of integration, the expressions for the strain measures themselves. Similarly, the same strategy is applied to the highly nonlinear inertia terms. Several examples have been considered in which it was observed that energy, linear momentum and angular momentum are conserved for both formulations even when considering very large number of time-steps. Next, 2D elasto-(visco)-plastic fiber co-rotational beams element and a planar co-rotational beam with generalized elasto-(visco)-plastic hinges at beam ends have been developed and compared against each other for impact problems. Numerical examples show that strain rate effects influence substantially the structure response.In the second part of this thesis, a geometrically exact 3D Euler-Bernoulli beam theory is developed. The main challenge in defining a three-dimensional Euler-Bernoulli beam theory lies in the fact that there is no natural way of defining a base system at the deformed configuration. A novel methodology to do so leading to the development of a spatial rod formulation which incorporates the Euler-Bernoulli assumption is provided. The approach makes use of Gram-Schmidt orthogonalisation process coupled to a one-parametric rotation to complete the description of the torsional cross sectional rotation and overcomes the non-uniqueness of the Gram-Schmidt procedure. Furthermore, the formulation is extended to the dynamical case and a stable, energy conserving time-stepping algorithm is developed as well. Many examples confirm the power of the formulation and the integration method presented.
|
|
| 10. |
- Chhang, Sophy, et al.
(author)
-
Energy-momentum method for nonlinear dynamic of 2D corotational beams.
- 2016
-
In: Eccomas 2016 Proceedings. - Athens : Computational Methods in Structural Dynamics & Earthquake Engineering. - 9786188284401
-
Conference paper (peer-reviewed)abstract
- This paper presents an energy-momentum method for nonlinear dynamics of 2D Bernoulli corotational beams. It is shown that the time stepping algorithm conserves energy, linear momentum and angular momentum. To be consistent in the corotational approach, cubic interpolations of Bernoulli element are employed to derive both inertia and elastic terms. The shallow arch strain definition is used to get an element which produce accurate results for less number of elements. To avoid membrane locking, we use a constant and average value of the axial strains. In addition, the energy-momentum method is used to preserve the conserving properties, which is able to maintain the stability and accuracy in a non-dissipative system for a long period. The midpoint velocities of kinematic fields and strains are used to tackle any non-linear form of strain displacement relations. Finally, two examples including large overall displacement are presented to illustrate the stability and efficiency of the proposed algorithms.
|
|
