Use of Lagrange multipliers to combine 1D variable kinematic finite elements

• An hierarchical, 1D, variable kinematic FE formulation is introduced.
• Lagrange multipliers are used to combine variable kinematic finite elements.
• Compact, thin-walled and bridge-like structures are considered.
• 1D variable kinematic models are able to detect complex strain–stress fields.

This paper deals with finite element problems that require different formulations in different subregions of the problem domain. Attention is focused on a variable kinematic, one-dimensional, finite element formulation which was recently introduced by the first author. Finite elements with different order of expansion over the cross-section plane are employed in different regions of the 1D domain. Lagrange multipliers are used to “mix” different elements. Constraints are imposed on displacement variables at a number of points whose location over the cross-section is a parameter of the method. The number and the location of the connection points can be modified until convergence is reached. The method is first assessed by encompassing sample problems and then it is applied to analyze a number of structures which requires different formulations in different regions. Compact, thin-walled and bridge-like sections are considered to show the effectiveness of the methodology proposed as well as its advantages to solve practical problems.