Complementarity Problems in Structural Engineering: An Overview

Bolzon, Gabriella

doi:10.1007/s11831-015-9158-8

Cited by 11 publications

(3 citation statements)

References 99 publications

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“…The formulation sets in within similar modelization attempts in the limit analysis of masonry constructions [63][64][65][66][67][68][69][70][71][72][73][74] and relies on a series of works in stating the optimiza- [75][76][77][78][79][80], as ruled by typical theoretical literature references [81][82][83][84][85].…”

Section: Least-thickness Optimization By a Complementarity Problem/mamentioning

confidence: 99%

Static Upper/Lower Thrust and Kinematic Work Balance Stationarity for Least-Thickness Circular Masonry Arch Optimization

Cocchetti

Rizzi

2020

J Optim Theory Appl

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This paper re-considers a recent analysis on the so-called Couplet–Heyman problem of least-thickness circular masonry arch structural form optimization and provides complementary and novel information and perspectives, specifically in terms of the optimization problem, and its implications in the general understanding of the Mechanics (statics) of masonry arches. First, typical underlying solutions are independently re-derived, by a static upper/lower horizontal thrust and a kinematic work balance, stationary approaches, based on a complete analytical treatment; then, illustrated and commented. Subsequently, a separate numerical validation treatment is developed, by the deployment of an original recursive solution strategy, the adoption of a discontinuous deformation analysis simulation tool and the operation of a new self-implemented Complementarity Problem/Mathematical Programming formulation, with a full matching of the achieved results, on all the arch characteristics in the critical condition of minimum thickness.

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Section: Least-thickness Optimization By a Complementarity Problem/mamentioning

confidence: 99%

Static Upper/Lower Thrust and Kinematic Work Balance Stationarity for Least-Thickness Circular Masonry Arch Optimization

Cocchetti

Rizzi

2020

J Optim Theory Appl

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“…A remarkable feature of such a formulation is the weak imposition of the material evolution equations at element level (instead of quadraturepoint level), thus recalling the notion of constitutive law of the finite element tracing back to Maier's work [54,55]. For elastoplasticity, a deeply explored strategy amounts at the adoption of the complementary mixed (CM) functional, initially proposed in [92], and after addressed in [79,11,49,57,13,12] (for an overview on complementarity problems in structural engineering, the reader is referred to [16]). That can be regarded as a reduced version of the return map functional, in which only the plastic multiplier field is interpolated among all internal variables, thus implying a weak element flow law.…”

Section: Mixed Variational Formulationsmentioning

confidence: 99%

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

Nodargi

2018

Arch Computat Methods Eng

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As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard displacement-based finite element formulations, attention is here focused on the use of mixed methods as approximation technique, within the small strain framework, for the mechanical problem of inelastic bidimensional structures. Despite a great flexibility characterizes mixed element formulations, several theoretical and numerical aspects have to be carefully taken into account in the design of a high-performance element. The present work aims at providing the basis for methodological analysis and comparison in such aspects, within the unified mathematical setting supplied by generalized standard material model and with special interest towards elastoplastic media. A critical review of the state-of-the-art computational methods is delivered in regard to variational formulations, selection of interpolation spaces, numerical solution strategies and numerical stability. Though those arguments are interrelated, a topic-oriented presentation is resorted to, for the very rich available literature to be properly examined. Finally, the performances of several significant mixed finite element formulations are investigated in numerical simulations.

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“…A concrete gravity dam (Bolzon, 2017) depicted in Fig. 5.6a) with a self-weight of 24 kN-m -3 was supported by a solid foundation and applied by the hydraulic pressure (water weight of 10 kN-m -3 ) at an upstream face.…”

Section: Example 2: Concrete Gravity Dammentioning

confidence: 99%

The performance of automatic adaptive edge-based smoothed finite element method in engineering mechanics applications

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The thesis investigates the performance of an edge-based smoothed finite element method (ES-FEM) combined with an automatic mesh refinement (AMR) algorithm to provide the solutions of in-plane elastic engineering mechanics applications. The ES-FEM adopts a strain smoothing technique over the edges adjoining the two adjacent triangular-shape meshes, whilst a layer of singular yet compatible five-node elements in addition to standard three-node ES-FEs can be employed to overcome the problems associated with stress singularity. The proposed framework enables the effective model construction of realistic engineering structures with complex geometry at modest computational resources. The AMR algorithm adopts the newest node bisection scheme that automatically sub-divides the parent critical elements into a suitable number of smaller children members at the longest edge of three-node elements overcoming the hang-node problems. The set of critical members is determined by the L2-norm error estimator functions defining the difference between the computed numerical von Mises stress solutions and recovery stress values. A number of illustrative, including classical benchmarks, examples were successfully processed by the proposed numerical analysis platform. These hence present the efficiency of the developed analysis framework in approximating the accurate elastic responses of structures under applied forces.

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Complementarity Problems in Structural Engineering: An Overview

Cited by 11 publications

References 99 publications

Static Upper/Lower Thrust and Kinematic Work Balance Stationarity for Least-Thickness Circular Masonry Arch Optimization

Static Upper/Lower Thrust and Kinematic Work Balance Stationarity for Least-Thickness Circular Masonry Arch Optimization

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

The performance of automatic adaptive edge-based smoothed finite element method in engineering mechanics applications

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