Time integration in the context of energy control and locking free finite elements

2000 ◽  
Vol 7 (3) ◽  
pp. 299-332 ◽  
Author(s):  
D. Kuhl ◽  
E. Ramm
Keyword(s):  
Finite Elements ◽  
Time Integration ◽  
Energy Control

scholarly journals Optimal control of robotic systems using finite elements for time integration of covariant control equations

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Juan Antonio Rojas-Quintero ◽  
Jorge Villalobos-Chin ◽  
Victor Santibanez
Keyword(s):  
Optimal Control ◽  
Finite Elements ◽  
Time Integration ◽  
Robotic Systems

scholarly journals Numerical modeling of reinforced concrete structures: static and dynamic analysis

2013 ◽  
Vol 66 (4) ◽  
pp. 425-430 ◽  
Author(s):  
Jorge Luis Palomino Tamayo ◽  
Armando Miguel Awruch ◽  
Inácio Benvegnu Morsch
Keyword(s):  
Reinforced Concrete ◽  
Numerical Model ◽  
Finite Elements ◽  
Dynamic Analysis ◽  
Time Integration ◽  
Great Accuracy ◽  
Constitutive Law ◽  
Published Data ◽  
Static And Dynamic Analysis ◽  
Plates And Shells

A numerical model using the Finite Element Method (FEM) for the nonlinear static and dynamic analysis of reinforced concrete (RC) beams, plates and shells is presented in this work. For this purpose, computer programs based on plasticity theory and with crack monitoring capabilities are developed. The static analysis of RC shells up to failure load is carried out using 9-node degenerated shell finite elements while 20-node brick finite elements are used for dynamic applications. The elasto-plastic constitutive law for concrete is coupled with a strain-rate sensitive model in order to take into account high loading rate effect when transient loading is intended. The implicit Newmark scheme with predictor and corrector phases is used for time integration of the nonlinear system of equations. In both cases, the steel reinforcement is considered to be smeared and represented by membrane finite elements. Various benchmark examples are solved with the present numerical model and comparisons with other published data are performed. For all examples, the path failure, collapse loads and failure mechanism is reproduced with great accuracy.

scholarly journals NUMERICAL SIMULATION OF A MASSIVE IMPACTOR FALLING ONTO A REINFORCED CONCRETE BEAM

2020 ◽  
Vol 82 (1) ◽  
pp. 5-15
Author(s):  
S.M. Gertsik ◽  
Yu.V. Novozhilov
Keyword(s):  
Finite Elements ◽  
Concrete Beam ◽  
Time Integration ◽  
Volumetric Strain ◽  
Failure Criteria ◽  
Tensile Failure ◽  
Low Velocity Impact ◽  
Isotropic Hardening ◽  
Elastoplastic Material ◽  
Low Velocity

The paper presents the results of numerically modeling the dynamics of a concrete beam reinforced by longitudinal rods and transversal frames of rods under the effect of a falling massive impactor. The dynamic behavior of the material of concrete is described using the Holmquist - Johnson - Cook model. The reinforcement of the beam is modeled by beam elements, using the bilinear model of elastoplastic material with isotropic hardening. Binding between the reinforcement and concrete is described by introducing additional kinematic equations that couple degrees of freedom of the related nods of the beam and volumetric finite elements. The mathematical model makes it possible to introduce additional failure criteria to predict propagation of tensile cracking. Pressure lower than the minimal one (failure only in the tension zone) and volumetric strain higher than the threshold value are taken as a criterion of tensile failure. Failure is modeled by removing elements from the computational pattern, when the above failure criteria are satisfied. The effect of accounting for failure on the response of the beam is analyzed. Numerical modeling is done using the finite-element method with explicit time integration in the LOGOS and LS-DYNA systems. Concrete is modeled using linear four-node finite elements with one integration point. The impactor is modeled as an absolutely solid body with a detailed description of the impacting end. The obtained results are compared with experimental data. It is demonstrated that the Holmquist - Johnson - Cook material model developed for analyzing high-velocity impacts can also be applied to problems of low-velocity impact.

Finite Elements in Time and Space

1969 ◽  
Vol 73 (708) ◽  
pp. 1041-1044 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Finite Elements ◽  
Linear Equations ◽  
Time Integration ◽  
Fixed Time ◽  
Time Interval ◽  
Structural Elements ◽  
Dynamic Problems ◽  
System Of Linear Equations ◽  
Interpolation Procedure ◽  
Variational Statement

The present paper seeks to apply the ideas of discretisation to time dependent phenomena. As a suitable variational statement we may use Hamilton's principle. In practise this means that the time is discretised into a set of finite elements which are taken to be the same for all structural elements. A finite element in time consists simply of a fixed time interval. In our present discussion we detail in particular the case when at the beginning and end of the time interval the generalised displacements and velocities are given. For dynamic problems this is the minimum of information required, but the technique may easily be extended to account for additional “timewise degrees of freedoms”. Introducing an appropriate interpolation procedure we may obtain the displacement and velocity at any instant of time. It is then possible to carry out in the variational statement the time integration explicitly and to obtain hence a system of linear equations. The method is extremely simple, since the time interpolation of all structural freedoms of an element in space is the same. We also demonstrate that the general case of a multi-degree of freedoms system can be made to depend on the matrices which describe the unidimensional motion of a mass point.

scholarly journals High-Order Time Integration in the p-Version of Finite Elements

PAMM ◽  
2010 ◽  
Vol 10 (1) ◽  
pp. 201-202
Author(s):  
Torben Netz ◽  
Stefan Hartmann
Keyword(s):  
Finite Elements ◽  
Time Integration ◽  
High Order ◽  
High Order Time

scholarly journals Rotation-Free Based Numerical Model for Nonlinear Analysis of Thin Shells

Buildings ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 657
Author(s):  
Hrvoje Smoljanović ◽  
Ivan Balić ◽  
Ante Munjiza ◽  
Viktor Hristovski
Keyword(s):  
Numerical Model ◽  
Finite Elements ◽  
Yield Criterion ◽  
Geometrical Nonlinearity ◽  
Time Integration ◽  
Triangular Element ◽  
Integration Scheme ◽  
Flow Rule ◽  
Thin Shells ◽  
Time Step

This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi-Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.

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