A curved quadrilateral element for static analysis of shells with geometric and material nonlinearities. (English) Zbl 0562.73064
Summary: A 48 degrees-of-freedom quadrilateral element, including the effect of both material and geometric nonlinearities, is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for the static nonlinear analysis of general shell structures. The element surface is described by variable-order polynomials in curvilinear co-ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co-ordinates. Without being confined to the assumption of axisymmetry, this formulation allows for the treatment of shells with a more general shape and with a complex spread of plastic zones. In the formulation for geometric nonlinearity, the total Lagrangian approach is adopted. Only small strains and small rotations are allowed. In the formulation for plastic deformation, the concept of a layered element model is used. In the inelastic range, the material is assumed to obey the Von Mises yield criterion and the Prandtl-Reuss flow rule. A tangential stiffness formulation is combined with the modified Newton-Raphson iteration method for the solution of nonlinear problems. A systematic choice of examples ranging from flat plates to cylindrical panels and to spherical caps is solved and compared with available solutions to evaluate the recommended formulations and procedures in terms of their accuracy and efficiency.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K15 | Membranes |
| 74B20 | Nonlinear elasticity |
| 74S99 | Numerical and other methods in solid mechanics |
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
Keywords:
degrees-of-freedom quadrilateral element; material and geometric nonlinearities; static nonlinear analysis of general shell structures; variable-order polynomials in curvilinear co-ordinates; bicubic Hermitian polynomials; total Lagrangian approach; small strains; small rotations; layered element model; Von Mises yield criterion; Prandtl-Reuss flow rule; tangential stiffness formulation; modified Newton-Raphson iteration method; accuracy; efficiencyReferences:
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