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Variable kinematics beam elements are formulated on the basis of a unified formulation (UF).
These beam elements are formulated from classical beam theory, with a basic assumption that "plane sections remain plane" during bending.
Elastically orthogonally refined asymmetric Timoshenko beam elements are formulated and used for the calculation of lower bounds to the natural frequencies of asymmetric beams by the method of separation of element spaces by contraction.
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Stiffness as well as mass matrices of the curved and the straight beam elements is formulated.
The incremental finite element method using linear Timoshenko beam elements is formulated by the total Lagrangian approach for the superelastic, large deformation analysis of SMA helical springs.
Based on the Refined Zigzag Theory (RZT), a class of efficient higher-order C0-continuous beam elements is formulated and numerically assessed.
The equilibrium equations of a straight beam element are formulated using an updated Lagrangian (UL) incremental description.
The shape functions of the beam element are formulated by solving the homogeneous Euler Lagrangian equations with corresponding boundary conditions of the beam element.
Based on the proposed model, an efficient C0-continuous beam element is formulated by adopting the anisoparametric interpolation strategy to avoid the shear locking phenomenon.
In both the methods, an equivalent rotational spring is used to model the local flexibility caused by an open crack and the respective damaged beam element is formulated.
The graded elements are formulated with continuously nonhomogeneous material property fields and compared to conventionally formulated homogeneous elements.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com