• Structural Engineering and Mechanics
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• v.41 no.6
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• pp.735-750
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• 2012

This paper presents a comparison between two different procedures to deal with the geometric nonlinear analysis of space trusses, considering its structural stability aspects. The first nonlinear formulation, called positional, uses nodal positions rather than nodal displacements to describe the finite elements kinematics. The strains are computed directly from the proposed position concept, using a Cartesian coordinate system fixed in space. The second formulation, called corotational, is based on the explicit separation between rigid body motion and deformed motion. The numerical examples demonstrate the performances and the convergence of the responses for both analyzed formulations. Two numerical examples were compared, including a lattice beam with postcritical behavior. Despite the two completely different approaches to deal with the geometrical nonlinear problem, the results present good agreement.

• Journal of Korea Game Society
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• v.18 no.1
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• pp.125-134
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• 2018

This paper presents a practical method to efficiently extract the rotational part of a $3{\times}3$ matrix that changes continuously in time. This is the key technique in the corotational FEM and the shape matching deformation popular in physics-based dynamic deformation. Recently, in contrast to the traditional polar decomposition methods independent of time, an iterative method was proposed that formulates the rotation extraction in a physics-based way and exploits an incremental representation of rotation. We develop an optimization method that reduces the number of iterations under the assumption that the maximum magnitude of the incremental rotation vector is limited within ${\pi}/2$. Realistic simulation of dynamic deformation employs a sufficiently small time step, and thus this assumption is not problematic in practice. We demonstrate the efficiency and practicality of our method in various experiments.