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Potential of Homogenized and Non-local Beam and Plate Theories in Ship Structural Design

The paper gives an overview of the recent development on application of homogenized, non-local beam and plate theories in design of marine structures. The homogenization considers all steps of the derivation of the prevailing differential equations from kinematics to equilibrium with external loading. This enables an accurate localization process that recovers the microstructural effects from the homogenized solution of the prevailing differential equations. Presently, the method is handle limit states of serviceability and ultimate strength. The theory is validated by full 3D-FE simulations on periodic beams and plates. The theory converges to the physically correct solutions in case of infinite and zero shear stiffness; especially the limit of zero shear stiffness is important as there the traditional Timoshenko beam theory (TBT) fails to predict the response correctly. We also show the case of plate under bi-axial loading where the bifurcation buckling solutions fail to predict correctly the physics, but the non-local framework is able to handle this case.

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