On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low-order methods for two model problems and nonlinear elastodynamics

Armero, F.; Romero, Ignacio

doi:10.1016/s0045-7825(00)00256-5

Cited by 114 publications

(130 citation statements)

References 25 publications

Supporting

Mentioning

124

Contrasting

Unclassified

Order By: Relevance

“…The proposed methods not only provide the correct and nieaningful energy balance for the system but show, as expected, excellent robustness as compared with standard implicit methods. We must stress that the added stability is obtained without any artificial numerical damping which, although commonly used for niultibody applications, often has the effect of breaking the symmetries of the problem and spoiling, for example, the conservation of angular momentum (Armero and Romero, 2001a).…”

Section: Introductionmentioning

confidence: 99%

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics

Orden

Romero

2012

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

A novel time integration scheme is presented for the numerical solution of the dynamics of discrete systems consisting of point masses and thermovisco-elastic springs. Even considering fully coupled constitutive laws for the elements, the obtained solutions strictly preserve the two laws of thermodynamics and the symmetries of the continuum evolution equations. Moreover, the unconditional control over the energy and the entropy growth have the effect of stabilizing the numerical solution, allowing the use of larger time steps than those suitable for comparable implicit algorithms. Proofs for these claims are provided in the article as well as numerical examples that illustrate the performance of the method.

show abstract

Section: Introductionmentioning

confidence: 99%

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics

Orden

Romero

2012

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

show abstract

“…The Green-Lagrange strain tensor is (15) and (16) are evaluated for α f = 1/2 without damping, such as ξ = 0, then the energy-momentum method by Simo and Tarnow [31] is recovered for VenantKirchhoff material. Additionally, the scheme presented here is only second-order accurate when ξ = 0, as remarked by Armero and Romero [2]. For verification and validation in the next section, this parameter is set to zero and is included in the above formulation for completeness.…”

Section: Discretisation Of Elastic Body Mechanicsmentioning

confidence: 99%

A constrained generalised- $$\alpha $$ α method for coupling rigid parallel chain kinematics and elastic bodies

Gransden

Bornemann²,

Rose

et al. 2015

Comput Mech

View full text Add to dashboard Cite

A problem arises from combining flexible rotorcraft blades with stiffer mechanical links, which form a parallel kinematic chain. This paper introduces a method for solving index-3 differential algebraic equations for coupled stiff and elastic body systems with closed-loop kinematics. Rigid body dynamics and elastic body mechanics are independently described according to convenient mathematical measures. Holonomic constraint equations couple both the parallel chain kinematics and describe the coupling between the rigid and continuum bodies. Lagrange multipliers enforce the kinetic conditions for both sets of constraints. Additionally, to prevent numerical inaccuracy from inverting stiff mechanical matrices, a scaling factor normalises the dynamic tangential stiffness matrix. Finally, example tests show the verification of the algorithm with respect to existing computational tests and the accuracy of the model for cases relevant to the problem definition.

show abstract

“…Other work focused on applying these algorithms to specific finite element formulations (beam and shell elements) [41,42,15,48] and multi-body systems [7,10,28]. Despite the achievement of unconditional stability, the energy conserving schemes still show difficulties for numerically stiff nonlinear problems [7, 1,2], and especially for snap-through buckling problems [31,32]. The energy conserving schemes fail to converge in the post-snap range with an acceptable time step, due to the lack of numerical dissipation for spurious high-frequency oscillations.…”

Section: Introductionmentioning

confidence: 99%

“…These algorithms involve a multistage computation per time step and require solving a larger system than those solved with classical schemes, due to the coupling between the displacement and velocity. Another approach is to construct the algorithm from an energy conserving integrator [32,30,1,2,36,27]. These algorithms are designed using a specialized approximation of the element stress tensor and the velocity to ensure a positive numerical damping.…”

Section: Introductionmentioning

confidence: 99%

A robust composite time integration scheme for snap-through problems

et al. 2015

View full text Add to dashboard Cite

A robust time integration scheme for snapthrough buckling of shallow arches is proposed. The algorithm is a composite method that consists of three sub-steps. Numerical damping is introduced to the system by employing an algorithm similar to the backward differentiation formulas (BDF) method in the last substep. Optimal algorithmic parameters are established based on stability criteria and minimization of numerical damping. The proposed method is accurate, numerically stable, and efficient as demonstrated through several examples involving loss of stability, large deformation, large displacements and large rotations.

show abstract

On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low-order methods for two model problems and nonlinear elastodynamics

Cited by 114 publications

References 25 publications

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics

A constrained generalised- $$\alpha $$ α method for coupling rigid parallel chain kinematics and elastic bodies

A robust composite time integration scheme for snap-through problems

Contact Info

Product

Resources

About