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In order to solve the so‐called consistently linearized eigenproblem in the frame of the Finite Element Method (FEM), the derivative of the tangent stiffness matrix with respect to the load parameter λ needs to be calculated. In this work, three schemes for calculation of are presented. The first scheme is based on an analytical expression for the first derivative...
Depending on whether or not bending and/or torsion are part of the prebuckling deformation state of elastic structures, the initial postbuckling behavior is either completely general or characterized by specific restrictions [1]. In this context, the term ‘completely general’ means (a) no restriction to monotonic improvement or deterioration of the initial postbuckling behavior in consequence of a...
Unless the hangers of arch bridges are sufficiently stiff, such bridges are imperfection sensitive [1]. Increasing the stiffness of the hangers, such structures eventually become imperfection insensitive. The mathematical definition of imperfection insensitivity follows from a series expansion of the dimensionless load parameter Δλ(κ, η), relative to the stability limit λ = λS, given as [2]
where...
Koiter's postbuckling analysis and the consistently linearized eigenvalue problem are used in sensitivity analysis of the postbuckling behavior of elastic structures. A classification of structures can be made on basis of the eigenvector of the eigenvalue problem. This classification distinguishes between structures with different quality of conversion from imperfections sensitivity into imperfection...
In the course of sensitivity analysis of the initial postbuckling behavior of elastic structures, a special case may occur which is referred to as zero‐stiffness postbuckling. The purpose of this paper is to present sufficient and necessary conditions for this special case which is associated with a favorable form of transition from imperfection sensitivity to imperfection insensitivity in the course...
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