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Material-Oriented Shape Functions for FGM Plate Finite Element Formulation.

ABSTRACT: A four-noded finite element of a moderately thick plate made of functionally graded material (FGM) is presented. The base element is rectangular and can be extended to any shape using a transformation based on NURBS functions. The proposed 2D shape functions are consistent with the physical interpretation and describe the states of element displacement caused by unit displacements of nodes. These functions depend on the FGM's material parameters and are called material-oriented. The shape function matrix is based on a superposition displacement field of two plate strips with 1D exact shape functions. A characteristic feature of the proposed formulation is full coupling of the membrane and bending states in the plate. The analytical form of the stiffness matrix and the nodal load vector was obtained, which leads to the numerical efficiency of the formulation. The element has been incorporated into Abaqus software with the use of Maple program. The finite element shows good convergence properties for different FGM models in the transverse direction to the middle plane of the plate. During derivation of the 2D plate element the formally exact 1D finite element for transverse nonhomogeneous FGM plate strip was developed.

SUBMITTER: Gilewski W

PROVIDER: S-EPMC7040622 | biostudies-literature | 2020 Feb

REPOSITORIES: biostudies-literature

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Material-Oriented Shape Functions for FGM Plate Finite Element Formulation.

Gilewski Wojciech W Pełczyński Jan J

Materials (Basel, Switzerland) 20200210 3

A four-noded finite element of a moderately thick plate made of functionally graded material (FGM) is presented. The base element is rectangular and can be extended to any shape using a transformation based on NURBS functions. The proposed 2D shape functions are consistent with the physical interpretation and describe the states of element displacement caused by unit displacements of nodes. These functions depend on the FGM's material parameters and are called material-oriented. The shape functi ...[more]

PMID: 32050599

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Project description:PurposeMinimally invasive transforaminal lumbar interbody fusion (MI-TLIF) is increasingly popular for the surgical treatment of degenerative lumbar disc diseases. The constructs intended for segmental stability are varied in MI-TLIF. We adopted finite element (FE) analysis to compare the stability after different construct fixations using interbody cage with posterior pedicle screw-rod or pedicle screw-plate instrumentation system.MethodsA L3-S1 FE model was modified to simulate decompression and fusion at L4-L5 segment. Fixation modes included unilateral plate (UP), unilateral rod (UR), bilateral plate (BP), bilateral rod (BR) and UP+UR fixation. The inferior surface of the S1 vertebra remained immobilized throughout the load simulation, and a bending moment of 7.5 Nm with 400N pre-load was applied on the L3 vertebra to recreate flexion, extension, lateral bending, and axial rotation. Range of motion (ROM) and Von Mises stress were evaluated for intact and instrumentation models in all loading planes.ResultsAll reconstructive conditions displayed decreased motion at L4-L5. The pedicle screw-plate system offered equal ROM to pedicle screw-rod system in unilateral or bilateral fixation modes respectively. Pedicle screw stresses for plate system were 2.2 times greater than those for rod system in left lateral bending under unilateral fixation. Stresses for plate were 3.1 times greater than those for rod in right axial rotation under bilateral fixation. Stresses on intervertebral graft for plate system were similar to rod system in unilateral and bilateral fixation modes respectively. Increased ROM and posterior instrumentation stresses were observed in all loading modes with unilateral fixation compared with bilateral fixation in both systems.ConclusionsTransforaminal lumbar interbody fusion augmentation with pedicle screw-plate system fixation increases fusion construct stability equally to the pedicle screw-rod system. Increased posterior instrumentation stresses are observed in all loading modes with plate fixation, and bilateral fixation could reduce stress concentration.

Dataset Information

Material-Oriented Shape Functions for FGM Plate Finite Element Formulation.

Publications

Material-Oriented Shape Functions for FGM Plate Finite Element Formulation.

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