Non-Linear Elastic |
 
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Non-Linear Elastic |
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You may specify a non-linear relationship for any or all of the bending stiffnesses EIyy and EIzz, the torsional stiffness GJ, and the axial stiffness EA. To use this option you define the relationship between “generalised stress” and “generalised strain”. The significance of “generalised stress” and “generalised strain” depends on the stiffness being defined. For bending stiffness, stress is bending moment M and strain is curvature κ, so the input is an M-κ curve. For torsional stiffness, stress is torque and strain is torsional strain (twist / length); while for axial stiffness, stress is axial force and strain is axial strain (extension / length).
Note that you can combine linear and non-linear specifications for the same element set; so for example you might specify a non-linear bending response, while GJ and EA are linear (single-valued).
A further option is available to you if you define a non-linear bending stiffness relation. Generally speaking, you input the same non-linear relationship for EIyy and EIzz. In the program terminology, the Symmetric non-linear bending model involves the computation of a single bending stiffness EI at any solution time based on the total curvature κ, with both EIyy and EIzz being set equal to EI. This means that the element stiffness will be same in any situation where κ is the same, regardless of the values of the individual curvature components.
An option to model Asymmetric non-linear bending behaviour is also provided. In this case, EIyy at any solution time is found from the curve you input for that stiffness term based on the instantaneous value of the corresponding local curvature term κy, and likewise EIzz is found based on instantaneous κz. This is true even if you input the same curve name for EIyy and EIzz. This can mean that bending response can differ for the same loading depending on element orientation; an orientation where κy and κz are non-zero can give a different response to an orientation with either κy or κz equal to zero.
It is possible to change material bending properties from linear to non-linear between successive analysis stages. Furthermore, the user-defined (non-linear) moment-curvature relationship used in a restart stage can be adjusted such that it is offset by moment-curvature values obtained from the preceding solution. Refer to Curvature Slippage for further information.
Refer to Non-linear Material Force Term for further information on how the Flexcom solver accounts for non-linear materials in the equilibrium equations.
•*MOMENT-CURVATURE is used to define moment-curvature curves for non-linear materials.
•*FORCE-STRAIN is used to define force-strain curves for non-linear materials.
•*TORQUE-TWIST is used to define torque-twist curves for non-linear materials.
•*NONLINEAR MODEL is used to specify a modelling approach for non-linear materials.