An FE-MPEC approach for limit load evaluation in the presence of contact and displacement constraints

Tangaramvong, Sawekchai; Tin‐Loi, F.

doi:10.1016/j.ijsolstr.2012.03.022

Cited by 11 publications

(3 citation statements)

References 32 publications

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“…A number of authors proposed different numerical methods (Livesley [33], Orduna & Lourenço [23], Gilbert et al [22], Tangaramvong and Tin-Loi [34]. The effects of friction on the static behavior of arch bridges has been discussed by Drosopoulos et al [35], whereas the effect of friction on the stability of masonry vaults has been studied by D'Ayala and coworkers [36,37], who assert that limit state analysis with finite friction allows to investigate two aspects of masonry vaults previously neglected: the possibility of sliding mechanisms between blocks and the importance of threedimensional stress fields in the equilibrium of complex vaults.…”

Section: High Friction Coefficientmentioning

confidence: 99%

Computational Methods for Masonry Vaults: A Review of Recent Results

Tralli¹,

Alessandri²,

Milani³

2014

TOCIEJ

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The paper concisely reviews the available numerical methods to analyze masonry vaults up to collapse, putting in evidence pros and limitations of each approach. To be reliable, any procedure adopted should take into account the distinctive aspects of masonry mechanical behavior, namely the scarce (or zero) tensile strength, the good compressive resistance and the observed formation of failure mechanisms constituted by rigid macro-blocks in mutual roto-translation. Classic no-tension material models disregard the little but not null tensile strength and make the hypothesis of (1) infinitely elastic behavior in compression and (2) isotropy, giving thus the possibility to deal with either semi-analytical approaches (especially for arches) or robust numerical procedures. More advanced but rather complex models are nowadays able to deal also with anisotropy induced by texture, little tensile strength and softening in tension, as well as finite strength in compression. Traditionally, limit analysis has proven to be the most effective for a fast and reliable evaluation of the load carrying capacity of vaulted masonry structures. Classic lower and upper bound theorems recall respectively the concepts of equilibrium and formation of failure mechanisms with rigid elements. The so-called Thrust Network Method moves its steps from lower bound theorem, whereas FE limit analysis approaches with rigid elements take inspiration from the upper bound point of view. An alternative to limit analysis is represented by traditional FEM combined with either elasto-plastic or damaging models with softening, usually adapted to masonry from other materials, which are capable of providing a large set of output numerical information but that still remain very demanding

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Section: High Friction Coefficientmentioning

confidence: 99%

Computational Methods for Masonry Vaults: A Review of Recent Results

Tralli¹,

Alessandri²,

Milani³

2014

TOCIEJ

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“…Therefore, it has been a difficult problem in the dynamic response analysis of lining structure in underground powerhouse. At present, the numerical method is mainly used to solve the dynamic contact problem, such as penalty function method [19], Lagrange multiplier method [20], numerical programming method [21], and contact element method [22]. However, these methods tend to have a large amount of computation, and the iteration does not usually converge.…”

Section: Introductionmentioning

confidence: 99%

Seismic Response Analysis of Concrete Lining Structure in Large Underground Powerhouse

Wang

Chen

Xiao

et al. 2017

Mathematical Problems in Engineering

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Based on the dynamic damage constitutive model of concrete material and seismic rock-lining structure interaction analysis method, the seismic response of lining structure in large underground powerhouse is studied in this paper. In order to describe strain rate dependence and fatigue damage of concrete material under cyclic loading, a dynamic constitutive model for concrete lining considering tension and shear anisotropic damage is presented, and the evolution equations of damage variables are derived. The proposed model is of simple form and can be programmed into finite element procedure easily. In order to describe seismic interaction characteristics of the surrounding rock and lining, an explicit dynamic contact analysis method considering bond and damage characteristics of contact face between the surrounding rock and lining is proposed, and this method can integrate directly without iteration. The proposed method is applied to seismic stability calculation of Yingxiuwan Underground Powerhouse, results reveal that the amplitude and duration of input seismic wave determine the damage degree of lining structure, the damage zone of lining structure is mainly distributed in its arch, and the contact face damage has great influence on the stability of the lining structure.

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“…Complementarity, the requirement that at least one of a pair of variables be at some limit, provides a framework for representing disjunctive behavior using a set of continuous equations. MPECs using complementarity constraints have found use in optimization problems in the fields of structural mechanics [4,5], chemical and process engineering [6][7][8][9], electric power generation [10], climate change [11], traffic networks [12], operations research [13], economics [14], and other fields [15,16].…”

Section: Introductionmentioning

confidence: 99%

A Continuous Formulation for Logical Decisions in Differential Algebraic Systems using Mathematical Programs with Complementarity Constraints

et al. 2016

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This work presents a methodology to represent logical decisions in differential algebraic equation simulation and constrained optimization problems using a set of continuous algebraic equations. The formulations may be used when state variables trigger a change in process dynamics, and introduces a pseudo-binary decision variable, which is continuous, but should only have valid solutions at values of either zero or one within a finite time horizon. This formulation enables dynamic optimization problems with logical disjunctions to be solved by simultaneous solution methods without using methods such as mixed integer programming. Several case studies are given to illustrate the value of this methodology including nonlinear model predictive control of a chemical reactor using a surge tank with overflow to buffer disturbances in feed flow rate. Although this work contains novel methodologies for solving dynamic algebraic equation (DAE) constrained problems where the system may experience an abrupt change in dynamics that may otherwise require a conditional statement, there remain substantial limitations to this methodology, including a limited domain where problems may converge and the possibility for ill-conditioning. Although the problems presented use only continuous algebraic equations, the formulation has inherent non-smoothness. Hence, these problems must be solved with care and only in select circumstances, such as in simulation or situations when the solution is expected to be near the solver's initial point.

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An FE-MPEC approach for limit load evaluation in the presence of contact and displacement constraints

Cited by 11 publications

References 32 publications

Computational Methods for Masonry Vaults: A Review of Recent Results

Computational Methods for Masonry Vaults: A Review of Recent Results

Seismic Response Analysis of Concrete Lining Structure in Large Underground Powerhouse

A Continuous Formulation for Logical Decisions in Differential Algebraic Systems using Mathematical Programs with Complementarity Constraints

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