Hysteretic Finite Elements for the Nonlinear Static and Dynamic Analysis of Structures

Triantafyllou, Savvas P.; Koumousis, V. K.

doi:10.1061/(asce)em.1943-7889.0000699

Cited by 29 publications

(19 citation statements)

References 44 publications

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“…While the micromodeling properties are accounted for in the inner (or finer) finite element mesh, the solution of the governing equations is performed on the outer (or coarser) mesh at a significantly reduced computational cost. Recently the method has been extended to account for the nonlinear dynamic response of heterogeneous domains [29] using the hysteretic finite element method at the fine scale [30]. Using this approach, inelasticity is introduced at the fine scale by formulating the evolution equations of plastic deformation within the framework of classical plasticity [31].…”

Section: Introductionmentioning

confidence: 99%

Towards a Multiscale Scheme for Nonlinear Dynamic Analysis of Masonry Structures with Damage

Triantafyllou

Chatzi²

2015

Computational Methods in Applied Sciences

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In this work, a three dimensional multiscale formulation is presented for the analysis of masonry structures based on the multiscale finite element formulation. The method is developed within the framework of the Enhanced Multiscale Finite Element Method. Through this approach, two discretization schemes are considered, namely a fine mesh that accounts for the micro-structure and a coarse mesh that encapsulates the former. Through a numerically derived mapping, the fine scale information is propagated to the coarse mesh where the numerical solution of the governing equations is performed. Inelasticity is introduced at the fine mesh by considering a set of internal variables corresponding to the plastic deformation accumulating at the Gauss points of each fine-scale element. These additional quantities evolve according to properly defined smooth evolution equations. The proposed formalism results in a nonlinear dynamic analysis method where the micro-level state matrices need only be evaluated once at the beginning of the analysis procedure. The accuracy and computational efficiency of the proposed scheme is verified through an illustrative example.

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Section: Introductionmentioning

confidence: 99%

Towards a Multiscale Scheme for Nonlinear Dynamic Analysis of Masonry Structures with Damage

Triantafyllou

Chatzi²

2015

Computational Methods in Applied Sciences

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“…(20) and (22), a consistent, smooth, modulus can also be defined, following the procedure introduced in [50]. The implications of the selection of an appropriate material modulus in conjunction with the solution procedure implemented are also discussed in [56].…”

Section: Multiaxial Modelling Of Hysteresismentioning

confidence: 99%

“…The exact form of the interpolation matrix [N σ ] depends on the element formulation and is also relevant to the stress recovery procedure implemented within the finite element formulation [56]. In this work the collocation points are chosen to coincide with the Gauss quadrature points where stresses are evaluated in standard FEM [65].…”

Section: 3mentioning

confidence: 99%

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A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

Triantafyllou

Chatzi

2014

Comput Mech

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A new multiscale finite element formulation is presented for nonlinear dynamic analysis of heterogeneous structures. The proposed multiscale approach utilizes the hysteretic finite element method to model the microstructure. Using the proposed computational scheme, the micro-basis functions, that are used to map the microdisplacement components to the coarse mesh, are only evaluated once and remain constant throughout the analysis procedure. This is accomplished by treating inelasticity at the micro-elemental level through properly defined hysteretic evolution equations. Two types of imposed boundary conditions are considered for the derivation of the multiscale basis functions, namely the linear and periodic boundary conditions. The validity of the proposed formulation as well as its computational efficiency are verified through illustrative numerical experiments.

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“…Therefore, searching for a simple, fast, and accurate earthquake response analysis method is an important area of research that engineers and scholars have been working towards for many years [6]. Currently, the dynamic response with a time history for a portal frame structure under the action of an earthquake is generally calculated by a finite element software [7,8], such as ANSYS [9] or MIDAS; unfortunately, for the complex civil structure with a large number of degrees of freedom, the computational work load is heavy, which cause long calculation times and low calculation efficiencies.…”

Section: Introductionmentioning

confidence: 99%

Study on the Seismic Response of a Portal Frame Structure Based on the Transfer Matrix Method of Multibody System

Ding

Zhuang

Wang

2014

Advances in Mechanical Engineering

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Portal frame structures are widely used in industrial building design but unfortunately are often damaged during an earthquake. As a result, a study on the seismic response of this type of structure is important to both human safety and future building designs. Traditionally, finite element methods such as the ANSYS and MIDAS have been used as the primary methods of computing the response of such a structure during an earthquake; however, these methods yield low calculation efficiencies. In this paper, the mechanical model of a single-story portal frame structure with two spans is constructed based on the transfer matrix method of multibody system (MS-TMM); both the transfer matrix of the components in the model and the total transfer matrix equation of the structure are derived, and the corresponding MATLAB program is compiled to determine the natural period and seismic response of the structure. The results show that the results based on the MS-TMM are similar to those obtained by ANSYS, but the calculation time of the MS-TMM method is only 1/20 of that of the ANSYS method. Additionally, it is shown that the MS-TMM method greatly increases the calculation efficiency while maintaining accuracy.

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Hysteretic Finite Elements for the Nonlinear Static and Dynamic Analysis of Structures

Cited by 29 publications

References 44 publications

Towards a Multiscale Scheme for Nonlinear Dynamic Analysis of Masonry Structures with Damage

Towards a Multiscale Scheme for Nonlinear Dynamic Analysis of Masonry Structures with Damage

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

Study on the Seismic Response of a Portal Frame Structure Based on the Transfer Matrix Method of Multibody System

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