Formulations and solution procedures for nonlinear structural analysis

Stricklin, J. A.; Haisler, W. E.

doi:10.1016/0045-7949(77)90067-0

Cited by 80 publications

(16 citation statements)

References 22 publications

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“…The non-negative second integral in (20) represents the elastic strain energy 6' W e that the structure would receive from the external agency promoting the disturbance in a hypothetical purely elastic regime. It is worth noting that d2 W e is strictly positive for any geometric perturbation not coincident with one generated by a virtual 6p alone.…”

Section: 2 Overall Stability and Instabilitiesmentioning

confidence: 99%

Effects of softening in elastic‐plastic structural dynamics

Maier

Perego

1992

Numerical Meth Engineering

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SUMMARYSoftening, understood as unstable behaviour of material or structural components, is considered herein for its possible consequences on the overall behaviour of discrete dynamic models of elastic-plastic beam structures, in the absence of geometric effects. It is shown that multiplicity of incremental solutions (response bifurcations) and manifestations of overall instability may occur. The bifurcated responses may exhibit different scenarios for the same excitation: e.g. shakedown or local damage up to failure. An insight into and criteria for such occurrences are achieved by formulating the rate and the finite increment problem as linear complementarity problems. Period doubling and deterministic chaos under harmonic excitation are observed when reversible (holonomic) softening behaviour is assumed. The strong sensitivity of the phenomena investigated with respect to the choice of the structural model is pointed out. The findings are elucidated by illustrative examples.

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Section: 2 Overall Stability and Instabilitiesmentioning

confidence: 99%

Effects of softening in elastic‐plastic structural dynamics

Maier

Perego

1992

Numerical Meth Engineering

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“…In order to determine the effect of increasing the support length a on the peak adhesive stresses and on the peak plate stresses an adhesively bonded T-joint with double support was analysed for different support lengths a of 15,20,25,30,40,60, and 80 mm based on the SSLD theory. The analyses were carried out for each of the boundary conditions shown in Fig.…”

Section: Effect Of Support Lengthmentioning

confidence: 99%

“…Still, many parameters ignored in the analytical approaches can be taken into account and more realistic solutions can be achieved. Wood and co-workers [14,15], Stricklin and co-workers [16][17][18][19][20], Carey [21], and Bathe and Cimento [22] are among those who have contributed to the development of the FEM including geometrically non-linear effects. More details can be found in Refs [4,23] and [24].…”

Section: Introductionmentioning

confidence: 99%

On the non-linear elastic stresses in an adhesively bonded T-joint with double support

Apalak¹

2002

Journal of Adhesion Science and Technology

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Structures consisting of single or more materials, such as adhesive joints, may undergo large displacements and rotations under reasonably high loads, although all materials are still elastic. The linear elasticity theory cannot predict correctly the deformation and stress states of these structures, since it ignores the squares and products of partial derivatives of the displacement components with respect to the material coordinates. When these derivatives are not small, these terms result in a non-linear effect called geometrical non-linearity. In this study, the geometrically non-linear stress analysis of an adhesively bonded T-joint with double support was carried out using the incremental nite element method. Different T-joint con gurations bonded to a rigid base and to a exible base were considered. For each con guration, linear and geometrically non-linear stress analyses of the T-joint were carried out and their results were compared for different horizontal and vertical plate end conditions. The geometrically non-linear analysis showed that the large displacements had a considerable effect on the deformation and stress states of both adherends and the adhesive layer. High stress concentrations were observed around the adhesive free ends and the peak adhesive stresses occurred inside the adhesive llets. The adherend regions corresponding to the free ends of the adhesive-plate interfaces also experienced stress concentrations. In addition, the effects of the support length on the peak adhesive and adherend stresses were investigated; increasing the support length had a considerable effect in reducing the peak adhesive and adherend stresses.

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“…It will cost a great deal of computational e!ort to obtain a long-term solution, especially for a system with many d.o.f. The pseudo-force method [22,23] and the incremental mode superposition technique [24,25] have also been used for non-linear response analysis, but both of them are still step-by-step time-marching scheme. The hybrid frequency}time domain (HFTD) method developed for soil}structure interaction analysis [26,27] has been shown to be an e$cient numerical procedure in solving non-linear transient responses.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Pseudo-Force/Laplace Transform Method for Non-Linear Transient Response of a Suspended Cable

Lou

2000

Journal of Sound and Vibration

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Formulations and solution procedures for nonlinear structural analysis

Cited by 80 publications

References 22 publications

Effects of softening in elastic‐plastic structural dynamics

Effects of softening in elastic‐plastic structural dynamics

On the non-linear elastic stresses in an adhesively bonded T-joint with double support

A Hybrid Pseudo-Force/Laplace Transform Method for Non-Linear Transient Response of a Suspended Cable

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