After discussion of related past work. a description is given of a B-spline finite strip method (FSM) for predicting the buckling stresses of rectangular sandwich plates. The core is represented as a three-dimensional solid in which the in-plane displacements vary quadratically through the thickness whilst the out-of-plane displacement varies linearly. The faceplates may in general be composite laminates which are represented, in turn. as either shear-deformable plates or classically-thin plates. The displacement field of a finite strip requires the representation of 12 (for shear-deformable faceplates) or eight (for thin faceplates) fundamental quantities over the strip plan area. with each quantity expressed as a summation of a series of products of longitudinal B-spline functions and crosswise shape functions. Full details are given of the development of elastic stillness and geometric stiffness matrices. The nature of the solution of the buckling problem is described and this incorporates multi-level sub-structuring. through the use of superstrips. This allows the efficient prediction of buckling stresses for both overall modes and highly-localised. wrinkling-type modes. but description of applications of the developed capability is deferred to the companion Part II paper.
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