Effects of softening in elastic‐plastic structural dynamics

Maier, G.; Perego, U.

doi:10.1002/nme.1620340120

Cited by 28 publications

(18 citation statements)

References 25 publications

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“…Ba zant et al (1987a,b) and Maier and Perego (1992), particularly with regard to the deduction of efficient numerical procedures (Ba zant and Mazars, 1990). In the context of concrete frame-like structures, two approaches have been suggested.…”

Section: Introductionmentioning

confidence: 99%

On materially and geometrically non-linear analysis of reinforced concrete planar frames

Bratina

Saje

Planinc

2004

International Journal of Solids and Structures

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A family of new beam finite elements for geometrically and materially non-linear static analysis of reinforced concrete planar frames is derived, in which strain measures are the only interpolated unknowns, and where the constitutive and equilibrium internal forces are equal at integration points. The strain-localization caused by the strainsoftening at cross-sections is resolved by the introduction of a 'short constant-strain element'. Comparisons between numerical and experimental results on planar frames in pre-and post-critical states show both good accuracy and computational efficiency of the present formulation.

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Section: Introductionmentioning

confidence: 99%

On materially and geometrically non-linear analysis of reinforced concrete planar frames

Bratina

Saje

Planinc

2004

International Journal of Solids and Structures

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“…The theoretical investigations from the viewpoint of applied mechanics have also been conducted (Herrmann, 1965;Ishida and Morisako, 1985;Maier and Perego, 1992;Araki and Hjelmstad, 2000;Williamson and Hjelmstad, 2001).…”

Section: Introductionmentioning

confidence: 99%

“…For SDOF systems, it is well known that, if the tangent stiffness becomes negative in a dynamic process, residual displacements increase. For MDOF systems, it has been shown that a negative eigenvalue of the tangent stiffness matrix leads to either the accumulation of deformation in a particular mode (Uetani and Tagawa, 1998) or the localization of deformation (Maier and Perego, 1992). Bernal (1998) indicated that a negative eigenvalue is a necessary condition of dynamic collapse.…”

Section: Introductionmentioning

confidence: 99%

Closed-Form Dynamic Stability Criterion for Elastic–Plastic Structures under Near-Fault Ground Motions

Kojima

Takewaki

2016

Front. Built Environ.

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A dynamic stability criterion for elastic-plastic structures under near-fault ground motions is derived in closed form. A negative post-yield stiffness is treated in order to consider the P-delta effect. The double impulse is used as a substitute of the fling-step near-fault ground motion. Since only the free vibration appears under such double impulse, the energy approach plays a critical role in the derivation of the closed-form solution of a complicated elastic-plastic response of structures with the P-delta effect. It is remarkable that no iteration is needed in the derivation of the closed-form dynamic stability criterion on the critical elastic-plastic response. It is shown via the closed-form expression that several patterns of unstable behaviors exist depending on the ratio of the input level of the double impulse to the structural strength and on the ratio of the negative post-yield stiffness to the initial elastic stiffness. The validity of the proposed dynamic stability criterion is investigated by the numerical response analysis for structures under double impulses with stable or unstable parameters. Furthermore, the reliability of the proposed theory is tested through the comparison with the response analysis to the corresponding onecycle sinusoidal input as a representative of the fling-step near-fault ground motion. The applicability of the proposed theory to actual recorded pulse-type ground motions is also discussed.

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“…This holds also in the present treatment, because the discretized pipeline-soil system involves a number of linearly elastic beam-elements (for the pipeline) with convex energy density and a number of soil-elements with nonconvex energy density [18]. Thus the existence of a solution in each time-step can be assured [12,21,22].…”

Section: H(t) = D(t) * Z(t) + D(t)mentioning

confidence: 99%

A numerical approach to the non-convex dynamic problem of pipeline-soil interaction under environmental effects

Liolios¹,

Georgiev²,

Liolios³

2012

AIP Conference Proceedings

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A numerical approach for a problem arising in Civil and Environmental Engineering is presented. This problem concerns the dynamic soil-pipeline interaction, when unilateral contact conditions due to tensionless and elastoplastic softening/fracturing behaviour of the soil as well as due to gapping caused by earthquake excitations are taken into account. Moreover, soil-capacity degradation due to environmental effects are taken into account. The mathematical formulation of this dynamic elastoplasticity problem leads to a system of partial differential equations with equality domain and inequality boundary conditions. The proposed numerical approach is based on a double discretization, in space and time, and on mathematical programming methods. First, in space the finite element method (FEM) is used for the simulation of the pipeline and the unilateral contact interface, in combination with the boundary element method (BEM) for the soil simulation. Concepts of the non-convex analysis are used. Next, with the aid of Laplace transform, the equality problem conditions are transformed to convolutional ones involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then a marching-time approach is applied and a non-convex linear complementarity problem is solved in each time-step.

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Effects of softening in elastic‐plastic structural dynamics

Cited by 28 publications

References 25 publications

On materially and geometrically non-linear analysis of reinforced concrete planar frames

On materially and geometrically non-linear analysis of reinforced concrete planar frames

Closed-Form Dynamic Stability Criterion for Elastic–Plastic Structures under Near-Fault Ground Motions

A numerical approach to the non-convex dynamic problem of pipeline-soil interaction under environmental effects

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