A new four-node rectangular element is proposed for the elastic analysis of plates in bending. This element has been formulated in view of the complex nature of existing nonlinear theory. The elastic theory developed in this paper has been derived in a form that allows a natural progression to plastic theory. The proposed method is mixed in the sense that moments and out of plane deflections are chosen as the unknowns. The solution matrix is developed from flexibility and equilibrium equations. Flexibility equations (expressing the relationship between the rotations and nodal moments) assume a partial quadratic moment field and are equated to obtain interelement compatibility. Equilibrium equations are formulated from virtual work expressions used in yieldline theory that are modified to include the twisting moment. For one-way plate action (single curvature), the solution is exact irrespective of the aspect ratio or the number of elements. For two-way action (double curvature), acceptable accuracy is achieved. Comparisons with exact solutions and the displacement method are included to indicate the accuracy of the proposed element.
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Columbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USAColumbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USA
Wang, Ji
Zhou, Bin
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Columbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USAColumbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USA
Zhou, Bin
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Liu, X. Sherry
Fields, Aaron J.
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Univ Calif San Francisco, Dept Orthopaed Surg, San Francisco, CA USA
Univ Calif Berkeley, Dept Mech Engn, Berkeley, CA 94720 USAColumbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USA
Fields, Aaron J.
Sanyal, Arnav
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Univ Calif Berkeley, Dept Mech Engn, Berkeley, CA 94720 USAColumbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USA
Sanyal, Arnav
Shi, Xiutao
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Columbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USAColumbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USA
Shi, Xiutao
Adams, Mark
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Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USAColumbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USA
Adams, Mark
Keaveny, Tony M.
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Univ Calif Berkeley, Dept Mech Engn, Berkeley, CA 94720 USAColumbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USA
Keaveny, Tony M.
Guo, X. Edward
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Columbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USAColumbia Univ, Dept Biomed Engn, Bone Bioengn Lab, New York, NY 10027 USA