Elastic-Plastic Analysis of Framed Structures using the Matrix Method

Ueda, Y.; Matsuishi, Masakatsu; Yamakawa, Taketo; Akamatsu, Taketo

doi:10.2534/jjasnaoe1968.1968.124_183

Cited by 12 publications

(7 citation statements)

References 1 publication

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“…Using the first order approximation of the residual via (35) and (36) and setting it equal to zero in combination with the consistency condition (37) gives the equation system …”

Section: Robust Return Algorithm Including Distributed Loadsmentioning

confidence: 99%

“…In the first iteration an estimate of ∆λ is calculated as well via (11) whereu t is replaced by ∆ũ t . Subsequently the residual is calculated via (35) and if the residual is sufficiently small and none of the yield conditions are violated, the predicted state is accepted. If the residual is not sufficiently small a midpoint state is determined by making half a step using (40) and (41) with rũ/2 and f y /2.…”

Section: Determine (∂mentioning

confidence: 99%

“…Flexibility formulations via a 6×6 equilibrium format was proposed in [34,35] for monotonic and cyclic plasticity models as well as in [26] including local imperfections. In order to model cyclic plasticity in frame structures more accurately [36] introduced a generalized formulation of the cyclic plasticity model from [37].…”

Section: Introductionmentioning

confidence: 99%

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A robust frame element with cyclic plasticity and local joint effects

Tidemann

Krenk

2018

Engineering Structures

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“…Using the first order approximation of the residual via (35) and (36) and setting it equal to zero in combination with the consistency condition (37) gives the equation system …”

Section: Robust Return Algorithm Including Distributed Loadsmentioning

confidence: 99%

Section: Determine (∂mentioning

confidence: 99%

See 1 more Smart Citation

A robust frame element with cyclic plasticity and local joint effects

Tidemann

Krenk

2018

Engineering Structures

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“…earthquake response analysis, taking into account some kind of degradation effect (Inglessis et al 1999;Kaewkulchai and Williamson 2004). The theory of plastic hinges was introduced in the late 1960's for both monotonic loading (Ueda et al 1968), and cyclic loading with large displacements (Ueda et al 1969). The elastic tangent stiffness matrix in a large displacement but small deformation theory was derived in (Oran 1973) with the use of an equilibrium format of the beam.…”

Section: Introductionmentioning

confidence: 99%

Cyclic Plastic Hinges with Degradation Effects for Frame Structures

Tidemann

Krenk

2017

J. Eng. Mech.

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A model of cyclic plastic hinges in frame structures including degradation effects for stiffness and strength is developed. The model is formulated via potentials in terms of section forces. It consists of a yield surface, described in a generic format permitting representation of general convex shapes including corners, and a set of evolution equations based on an internal energy potential and a plastic flow potential. The form of these potentials is specified by five parameters for each generalized stress-strain component describing: yield level, ultimate stress capacity, elastic and elasto-plastic stiffness, and a shape parameter. The model permits gradual changes in stiffness and strength parameters via damage-based degradation. The degradation effects are introduced in the energy and flow potentials and result in additional evolution equations for the corresponding strength and stiffness parameters. The cyclic plastic hinges are introduced into a six-component equilibrium-based beam element, using additive element and hinge flexibilities. When converted to stiffness format the plastic hinges are incorporated into the element stiffness matrix. The cyclic plastic hinge model has been implemented in a computer program and used for analysis of some simple structures illustrating the characteristic features of the cyclic response and the accuracy of the proposed model.

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“…Hence some kind of correction has to be applied on the magnitude of load increments. When Mises yield criterion is applied to plane stress problems, such a load magnification factor can be determined from the following equation : ( 4 ) where a: load magnification factor ay, rxy: stress components at the (n 1)th step Jax, Jay, 4rxy : increments of stress components at the nth step : yield stress of the material From Eq. ( 4 ), a is evaluated in the following form : It is known that the load magnification factor, a, is a function of the stress, (a), at the (n-1)th step, the stress increment, {Jo.…”

Section: Introductionmentioning

confidence: 99%

Reanalysis of Elasto-Plastic Structural Problems using Sensitivities

Yao

Fujikubo

Rahim

et al. 1991

J. SNAJ, Nihon zousen gakkai ronbunshu

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SummaryThis paper describes a procedure to predict the elasto-plastic responses of structures within the framework of the finite element method when design variables are changed. Reanalysis technique was used applying the Taylor Series ExpansionMethod with the results of sensitivity analysis.In the incremental finite element analysis, the load magnification factor is usually introduced to control the load increments so that yielding of individual elements takes place exactly. In sensitivity analysis, sensitivity of the load magnification factor with respect to the design variable was newly derived. In this connection, the sensitivity of elasto-plastic responses with respect to the yield stress of the material was also derived.Some sample calculations were performed on plane truss, plane frame and plane stress problems. The results proved the rationality of the proposed method. The reanalysis solution was much improved by considering the sensitivity of the load magnification factor although the computational time for sensitivity analysis increases. The limit of changes in design variables was also discussed to get rational reanalysis solutions. IntroductionIn the optimal design of structures, it is essential to know the change in objective and constraint functions with respect to design variables. For this purpose, sensitivity analysis and reanalysis are generally performed, which occupy a major part in optimization procedures.A number of research works on sensitivity analysis and reanalysis have been performed regarding the linear elastic problems. Contrary to this, those for the nonlinear problems are very few."' Regarding elasto-plastic plane stress problems, the authors developed the fundamental procedure of sensitivity analysis within the framework of the finite element method' In that paper, the coordinates of nodal points and the thickness were taken as the design variables, and the first and second-order sensitivities of stress components and nodal displacements were derived. A series of reanalyses was also performed applying the Taylor Series Expansion Method. The first and second-order sensitivities were evaluated with good accuracy. However, there existed large differences between the results of reanalysis and the exact solutions especially when the design variables were largely changed.

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Elastic-Plastic Analysis of Framed Structures using the Matrix Method

Cited by 12 publications

References 1 publication

A robust frame element with cyclic plasticity and local joint effects

A robust frame element with cyclic plasticity and local joint effects

Cyclic Plastic Hinges with Degradation Effects for Frame Structures

Reanalysis of Elasto-Plastic Structural Problems using Sensitivities

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