Instability investigation for rotating thin spherical membrane

Zhou, Yang; Nordmark, Arne; Eriksson, Anders

doi:10.1016/j.ijnonlinmec.2017.09.004

Cited by 2 publications

(4 citation statements)

References 41 publications

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“…The main difference is the systematic distinction among the added equations, as representing either physical constraints or selector conditions in the multi-parametric solution space. Following [46], the non-linear set of equations to solve for one equilibrium state is stated as…”

Section: Methodsmentioning

confidence: 99%

“…In many relevant problems, the static equilibrium solutions should fulfil additional physical constraints. These could, for instance, be a prescribed displacement relation, or a specified volume of liquid in a liquid-pressurized closed membrane, when pressure is used as the load parameter [46]. In examples below, physical constraints are also used to restrain rigid body movements with an objective method.…”

Section: Physical Constraintsmentioning

confidence: 99%

“…(6), may contain contributions from W p , W f and ΔW (if the penalty functions g are not linear in displacements), but not from ΔW c . It is noted that a particular constraint can be stated in several different forms g c , but as discussed in [46], physical constraints can -and should, for computational reasonsbe formulated to give a symmetric Jacobian. This also comes automatically when the problem formulation starts from a total energy expression, when the Jacobian is symmetric in the sense that…”

Section: Differential Responsementioning

confidence: 99%

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Constrained stability of conservative static equilibrium

Eriksson

Nordmark

2019

Comput Mech

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Modelling of static structural stability problems is considered. Focus is set on problems where passive physical constraints affect the response to applied forces, and where more than one free parameter describes the setting. The existence of vibration frequencies at equilibrium states is investigated, as an indication of stability. The relevant Jacobian matrix is developed, with an emphasis on the necessity to formulate the constraint equations from an energy form in a conservative problem. The corresponding mass matrix is introduced, with zero mass contribution from constraint equations. Three different forms of the relevant Jacobians are considered, and alternative methods for the eigenvalue extraction given. Stability is discussed in a context of generalized equilibrium problems, where auxiliary parameters and equations can be included in a continuation setting. Examples show the formulation, implementation and interpretation of stability.

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Section: Methodsmentioning

confidence: 99%

Section: Physical Constraintsmentioning

confidence: 99%

Section: Differential Responsementioning

confidence: 99%

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Constrained stability of conservative static equilibrium

Eriksson

Nordmark

2019

Comput Mech

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“…Therefore, the above equations must be modified to combine gravitational acceleration with radial acceleration. Investigations regarding the rotation of thin membranes, including fluids, and their influence on stability can be found in Reference 42.…”

Section: Realistic Modeling Of Gas‐fluid‐structure Interaction and Li...mentioning

confidence: 99%

Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

Schweizerhof,

Konyukhov

2024

Numerical Meth Engineering

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Load modeling in nonlinear statics, particularly incorporating large deformations differs significantly from the treatment in linear analysis. As in structural dynamics masses in a gravity field generate the loading, their location, and their modifications within the deformation process must be considered in a nonlinear simulation. A specific view besides loading by masses is on gas and fluid interaction with structures. In addition, load control using specifically designed algorithms is evaluated with respect to realistic applications. Within the load modeling an unavoidable, however side aspect, is the general discussion about the so‐called follower forces and non‐conservative loading. As an example of real‐world applications, the specifics of inflated rubber dams are presented.

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Instability investigation for rotating thin spherical membrane

Cited by 2 publications

References 41 publications

Constrained stability of conservative static equilibrium

Constrained stability of conservative static equilibrium

Some remarks on load modeling in nonlinear structural analysis–Statics with large deformations–Consistent treatment of follower load effects and load control

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