A mesh-geometry based method for coupling 1D and 3D elements

When conducting a finite element analysis (FEA) one way to reduce the total number of degrees of freedom is to use a mixed-dimensional model. Using beam elements to model long and slender components can significantly reduce the total number of elements. Problems arise when trying to connect elements with different dimensions in part due to incompatible degrees of freedom between different types of finite elements. This paper focuses on problems that occur in coupling beams and solids, which means coupling 1D and 3D finite elements. This paper presents a mesh-based solution to these problems only using specific arrangements of classical 1D and 3D finite elements without requiring the use of additional constraint equations. Two alternative solutions are detailed, evaluated and compared in this paper through series of computational experiments. The implementation of both solutions is also presented and involves mesh and geometry processing operations along with an adaptation of boundary representation (BREP) classical data structures.

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