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Non‐linear dynamic analysis of axisymmetric shells
Author(s) -
Nagarajan S.,
Popov E. P.
Publication year - 1975
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620090304
Subject(s) - rotational symmetry , finite element method , constitutive equation , viscoplasticity , displacement (psychology) , degenerate energy levels , classical mechanics , lagrangian , equations of motion , mathematics , dynamic relaxation , linear elasticity , mathematical analysis , variational principle , mechanics , physics , geometry , structural engineering , engineering , psychology , quantum mechanics , psychotherapist
Incremental equations of motion are derived from a Lagrangian variational formulation for the large displacement elastic‐plastic and elastic‐viscoplastic dynamic analysis of deformable bodies. The material constitutive behaviour is described in terms of the symmetric Piola–Kirchhoff stress and Lagrangian strain tensors. Degenerate isoparametric elements, permitting relaxation of the Kirchhoff–Love hypothesis, are used in a finite element formulation specialized for the analysis of shells of revolution subjected to axisymmetric loading. The linearized incremental equations of motion are solved using direct integration procedures, with added accuracy obtained from application of equilibrium correction at each step. The effectiveness of the numerical techniques is illustrated by the dynamic response analyses carried out on a shallow spherical cap subjected to uniform external step pressure loadings.