3D Warping in FourBar Laminated Linkages
Abstract
This paper deals with the evaluation of the componentlaminate loadcarrying capacity, i.e., to calculate the loads that cause the failure of the individual layers and the componentlaminate as a whole in fourbar mechanism. The componentlaminate loadcarrying capacity is evaluated using the TsaiWuHahn failure criterion for various layups. The reserve factor of each ply in the componentlaminate is calculated by using the maximum resultant force and the maximum resultant moment occurring at different time steps at the joints of the mechanism. Here, all component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular crosssections. They could, in general, be pretwisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3D elasticity theory. The component problems are thus split into 2D analyses of reference beam crosssections and nonlinear 1D analyses along the three beam reference curves. For the thin rectangular crosssections considered here, the 2D crosssectional nonlinearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thinwalled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear crosssectional analysis. Such closedform solutions are used here in conjunction with numerical techniques for the rest of the problem to predict more quickly and accurately than would otherwise be possible. Local 3D stress, strain and displacement fields for representative sections in the componentbars are recovered, based on the stress resultants from the 1D global beam analysis. A numerical example is presented which illustrates the failure of each componentlaminate and the mechanism as a whole.
 Publication:

Icnaam 2010: International Conference of Numerical Analysis and Applied Mathematics 2010
 Pub Date:
 September 2010
 DOI:
 10.1063/1.3497941
 Bibcode:
 2010AIPC.1281.1284P
 Keywords:

 functional analysis;
 matrix algebra;
 shear strength;
 partial differential equations;
 02.30.Sa;
 02.10.Yn;
 62.20.de;
 02.30.Jr;
 Functional analysis;
 Matrix theory;
 Elastic moduli;
 Partial differential equations