ABSTRACT of the Doctoral Thesis

## Finite Strip Formulations for Strength, Buckling and Post-Buckling Analysis of Stiffened Plates

### by Xinyu Wang (1994)

Thin-walled plate structures have become very popular in structural engineering due to their high strength-to-weight ratios. For precise solutions in structural analyses, the finite element method is well established and is regarded as a most powerful and versatile tool. For a certain group of problems, such as prismatic plate assemblies, an usual finite element analysis may be extravagant. Among many attempts at efficient analysis of such class of problems, the finite strip method is considered to be appealing.

The finite strip method can be considered as finite element method using a special element: a strip. The basic philosophy is to discretize the structures into longitudinal (or - in the case of shells of revolution - circumferential) strips and interpolate the behaviour in the longitudinal direction by harmonic functions and in the transverse direction by polynomial functions. Many research activities took place in this area investigating the applicability and developing many useful extensions. However, there are still the necessity and capability of further improvements, as shown in this present work.

In this work finite strip formulations are carried out, incorporating the effect of geometrical nonlinearity as well as buckling of simply supported stiffened plates. A FORTRAN program PIRTS is developed based on these formulations. Special consideration is given to the stability problem. The single term approach, which is widely used in buckling analysis, has the advantage of economy. However, in some cases, this approach yields buckling loads which are much larger than the actual ones. The algorithm used in PIRTS allows for the combination of single term approach with the complete (coupled) solution which makes possible efficient and accurate predictions of buckling loads as well as buckling modes. The complete solution procedure can be employed to generate correct solutions when the single term approach is invalid.

Considering geometrical nonlinearities, vigorous analytical calculations and programming in deriving the expressions for stiffness matrices and vectors of internal nodal forces become inevitable. The advantage of uncoupling between Fourier terms disappears unless special stress distributions are assumed, i.e. constant stresses along strip length. Otherwise the large scale of coupled equations makes the application of the finite strip method to nonlinear analysis less attractive. An incremental successive iterative technique is developed, which employs a Newton-Raphson procedure to solve the decoupled equations, with the errors from decoupling and linearization being eliminated simultaneously at each iteration step. This technique leads to a significant reduction in computational effort while flexible arrangements of loading are allowed for.

The foregoing algorithms are used for the calculation of two distinct design parameters: effective breadth of beam flanges under bending and effective width of postcritically buckled stiffened plates. The effective breadth of stiffened plates shows the effectiveness of the plate as a component of a beam in bending. That is to say, the shear lag phenomenon is studied. The linear finite strip solutions for effective breadth are compared with analytical results in the literature. For the effective width, the axial compressed stiffened plates in the postbuckling range are studied. Numerically computed results are compared with those derived from some well known empirical formulae (e.g., von-Karman effective width formula, Marguerre formula, Stowell Formula, etc.).

The program PIRTS has also access to powerful postprocessing tools and has the advantage of simplicity in input data preparation. Typical examples show the applicability of the developed finite strip formulations.

revised 951214 (hjb)