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Second-Order Structural Analysis With One Element Per Member, Jesse William Lyon

Theses and Dissertations

In this thesis, formulas for the local tangent stiffness matrix of a plane frame member are derived by differentiating the member resistance vector in the displaced position. This approach facilitates an analysis using only one element per member. The formulas are checked by finite difference. The derivation leads to the familiar elastic and geometric stiffness matrices used by other authors plus an additional higher order geometric stiffness matrix. Contributions of each of the three sub-matrices to the tangent stiffness matrix are studied on both the member and structure levels through two numerical examples. These same examples are analyzed three different …