Modeling of Inelastic Rocking Bodies under Cyclic Loading

Avgenakis, Evangelos; Psycharis, Ioannis N.

doi:10.1061/(asce)em.1943-7889.0001751

Cited by 15 publications

(11 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The displacement vector at the rocking end due to the resultant forces contribution, u r = [δ r , θ 1r ] T , can be proven [22] that is given by the following equation:…”

Section: Displacements Due To the Resultant Forcesmentioning

confidence: 99%

“…This is why an approximate determination of the region boundaries is applied. Due to space reasons, the proof of the methodology is not given here, but can be found in [22]. The necessary region boundaries and correct strain and additional displacement distributions inside each interval are calculated as follows:…”

Section: Approximate Determination Of Region Boundariesmentioning

confidence: 99%

“…For given shear stress distribution boundaries, the displacements u tn = [δ tn , θ tn ] T of the rocking end induced by a parabolic distribution with t = 1 can be calculated using the formulas found in [22]. For the value of t calculated with Eq.…”

Section: Displacements Due To the Self-equilibrating Shear Stressesmentioning

confidence: 99%

“…The contribution of the self-equilibrating normal stresses is the most cumbersome to calculate and is described in [22]. The procedure involves decomposing the normal stress distribution into triangular and trapezoidal normal loads.…”

Section: Displacements Due To the Self-equilibrating Normal Stressesmentioning

confidence: 99%

See 3 more Smart Citations

A Macro-Element Formulation for the Response of Inelastic Rocking Bodies Under Cyclic Loading

Avgenakis¹,

Psycharis²

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

Self Cite

View full text Add to dashboard Cite

In this paper, a macroelement for the prediction of the response of inelastic rocking bodies is proposed, which can be used in cyclic loading simulations. The ideas presented for the elastic rocking element formulation in previous works by the authors are extended here to the inelastic material case. Thus, apart from the deformability along the height of the body, the proposed macroelement also takes into account the inelastic deformations near the rocking interface, which is considered crucial for the accurate determination of the rocking response of deformable rocking bodies. Due to the partial loading of the rocking interface, nonlinear stress distributions develop across the rocking interface, which produce additional displacements to those predicted by the technical theory of bending. Taking these and the additional plastic displacements due to material nonlinearity into account, the correct stress distribution is determined based on the target displacements. The pushover curves derived with the proposed macroelement for characteristic problems are presented, while comparison is made against experimental results from the literature, showing satisfactory accuracy. 4719 COMPDYN 2019 7 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.

show abstract

“…The displacement vector at the rocking end due to the resultant forces contribution, u r = [δ r , θ 1r ] T , can be proven [22] that is given by the following equation:…”

Section: Displacements Due To the Resultant Forcesmentioning

confidence: 99%

Section: Approximate Determination Of Region Boundariesmentioning

confidence: 99%

Section: Displacements Due To the Self-equilibrating Shear Stressesmentioning

confidence: 99%

Section: Displacements Due To the Self-equilibrating Normal Stressesmentioning

confidence: 99%

See 2 more Smart Citations

A Macro-Element Formulation for the Response of Inelastic Rocking Bodies Under Cyclic Loading

Avgenakis¹,

Psycharis²

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

Self Cite

View full text Add to dashboard Cite

show abstract

“…The idealized systems discussed above assume that the structure is rigid—a questionable assumption as the size of the blocks increases. Figure 6 shows the force‐deformation curve of a rocking structure, when its deformability (or when the deformability of the underlying soil) is taken into account 43–56 . In this case, the pre‐uplift displacement is not zero but takes a finite value u up .…”

Section: Equivalent Description Of Rocking Systems With Nsbe Systemsmentioning

confidence: 99%

Simplified analysis of bilinear elastic systems exhibiting negative stiffness behavior

Manzo

Vassiliou

2020

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

This work studies the dynamics of the Negative Stiffness Bilinear Elastic (NSBE) oscillator. Such a mathematical idealization can be used to describe deformable rocking systems equipped with restraining tendons or with curved extensions of their bases. First, this paper establishes the characteristic quantities of the bilinear system to make it equivalent to the actual rocking structures. Then, it proceeds by proposing a simpler "equivalent" system that can be used to study the behavior of the NSBE. The equivalent system is not some linear elastic oscillator but a bilinear elastic system with zero stiffness of the second branch: the Zero Stiffness Bilinear Elastic (ZSBE) system. ZSBE is useful because it needs one parameter less than NSBE to be defined. Next, "Equal Displacement" and "Equal Energy" rules that provide estimates of the maximum displacement of the NSBE based on the response of the ZSBE are defined. The concept is similar to the RμΤ relations that provide estimates of the response of bilinear yielding systems based on the response of an equivalent linear elastic system, with one major difference: it does not resort to a linear elastic system but to the ZSBE. The proposed methodology is applied on the FEMA P695 ground motions scaled at three different levels. The results show that ZSBE is a good proxy of NSBE and, hence, indicate that an exhaustive study of the ZSBE is useful for the design of rocking structures.

show abstract

An integrated macroelement formulation for the dynamic response of inelastic deformable rocking bodies

Avgenakis

Psycharis

2020

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

SummaryThis paper presents a macroelement formulation for the prediction of the planar dynamic response of inelastic deformable rocking bodies. The formulation is based on a previous macroelement developed by the authors able to describe the cyclic response of inelastic rocking bodies, which takes into account the deformability both along the height of the member, as well as near the rocking end. Modifications of this formulation to account for other motion modes of rocking members during their dynamic response, namely, sliding and upthrow, as well as modifications to account for damping in a uniform manner during the whole motion, including impacts, are introduced. The dynamic response predicted by the macroelement for free‐standing rigid and deformable rocking bodies is presented and compared with existing theoretical solutions, and the effect of deformability, damping, inelasticity, and friction on the response is discussed.

show abstract

Modeling of Inelastic Rocking Bodies under Cyclic Loading

Cited by 15 publications

References 39 publications

A Macro-Element Formulation for the Response of Inelastic Rocking Bodies Under Cyclic Loading

A Macro-Element Formulation for the Response of Inelastic Rocking Bodies Under Cyclic Loading

Simplified analysis of bilinear elastic systems exhibiting negative stiffness behavior

An integrated macroelement formulation for the dynamic response of inelastic deformable rocking bodies

Contact Info

Product

Resources

About