E. P. Popov

University of California, Berkeley, Berkeley, California, United States

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Publications (6)8.05 Total impact

  • S. Nagarajan, E. P. Popov
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    ABSTRACT: The subject of this paper is the finite element analysis of axisymmetric solids subjected to axisymmetric static and dynamic loading, and taking into account material as well as geometric non-linearities. A general Lagrangian formulation forms the basis for the incremental equations of motion which are solved using direct integration methods. Solution accuracy is improved by applying equilibrium correction loads at each step. Finite element discretization is achieved through the use of quadrilateral plane stress and axisymmetric elements with incompatible modes added for improvement of the element flexural characteristics. Several numerical examples are presented to demonstrate the effectiveness of the developed computer program.
    Earthquake Engineering & Structural Dynamics 01/2007; 3(4):385 - 399. · 1.90 Impact Factor
  • S. Nagarajan, E. P. Popov
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    ABSTRACT: 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.
    International Journal for Numerical Methods in Engineering 06/2005; 9(3):535 - 550. · 2.06 Impact Factor
  • E. P. Popov, P. Sharifi
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    ABSTRACT: A refined axisymmetric curved finite element for the analysis of thin elastic-plastic shells of revolution is described in the paper. The improved element is obtained by employing cubic polynomials in terms of local Cartesian co-ordinates for the assumed in-plane and out-of-plane displacements. This introduces into the solution two internal degrees of freedom in the cord direction of each element. These internal degrees of freedom are removed by static condensation before assembling the individual element stiffness matrices, and are subsequently recovered after the nodal displacements are obtained. On comparison with the previous formulation, this procedure greatly improves the accuracy of the solution especially with regards to in-plane stress-resultants at discontinuities in the meridional curvature and interelement equilibrium of forces. The latter fact makes it possible to analyse shells with a discontinuous meridional slope. In using this element, improvement in the convergence of the elastic-plastic solutions has also been observed.Several examples illustrate the quality of solutions. The reported study is limited to axisymmetric loadings cum boundary conditions.
    International Journal for Numerical Methods in Engineering 06/2005; 3(4):495 - 508. · 2.06 Impact Factor
  • S. Nagarajan, E.P. Popov
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    ABSTRACT: A general formulation of large deformation analysis of plastic and viscoplastic problems is presented first. The equilibrium equations are derived from an incremental variational formulation using the Lagrangian mode of description of motion. The symmetric Piola-Kirchhoff stress and Lagrangian strain are used in all the constitutive relations. Using degenerate isoparametric elements, permitting relaxation of the Kirchhoff-Love hypothesis, the procedure is specialized for the finite element analysis of shells of revolution subjected to axisymmetric loading. A modified incremental method, which applies an equilibrium correction at each step, is used for the solution of the linearized incremental equilibrium equations. Two approaches are presented for adapting the viscoplasticity formulation to provide inviscid plasticity solutions- one involving the extrapolation of results as the viscosity coefficient tends to infinity, and the other in which plasticity solutions are obtained by using time as an artifice in the viscoplastic analysis until equilibrium states are achieved at each succeeding load level. A detailed study of the nonlinear behavior of a torispherical pressure vessel is presented to illustrate the effectiveness of the numerical techniques.РефератB пepBый pAз дAeтcя oбшAя фopмyлиpoBкA AнAлизA бoльщич дeфopмAций для плAcтичecкич и BязкoнлAcтнчecкнч зAдAч. oпpeдeляyтcя ypABнeния pABнoBecия нз BApиAциoннoй фopмyлиpoBки пpнpAщeния, нA ocнoBe cпocoбA ЛAгpAнжA oпиcAння дBнжeния. Bo Bceч кoнcтнтyтиBныч зABиcимocтяч нpимeняютcя cиммeтpичecкoe нAцpяжeниe Пиoля-КиpчгoффA и дeфopмAция ЛAгpA нжA. Пyтeм иcпoльзoBAния Bыpoждeнныч изoпApA мeтpнчecкич элeмeнтoB, кoтopыe дAкoт Boзмoжнocть peлякcAцни гипoзы КиpчгoффA-ЛABA, cпeциAлизиpyeтcя пpoцecc pAcчeтA для AнAлизA кoнeчнoгo элeмeнтA. oбoлoчeк BpAщeния, пoдBepжeнныч дeйcтBию ocecнммeтpнчecкoй нAгpyзкн. Для peщeния лннeApизoBAнньич ypABнeний pABнoBecия для пpнpAщeния пpимeняeтcя пpeoбpAзoBAнный мeтoд нpиpAщeния, кoтopый иcпoльзyeт иcпpABлeниe pABнoBecня для кAждoгo щAгA. ДAютcя дBA пoдчoды к peщeнию для пpнcпocoблeння фopмyлнpoBки B pAмкAч BязкoплAcтичпocти, c цeлью иcпoльзoBAння нeBязкич peщeний тeopни плAcтичнocтн, oдин, зAключAющий B ceбя экcтpAпoляцию peзyльтAтoB, кoгдA кoэффициeнт Bязкocти cтpeмитcя к бecкoнeчнocти и дpyтoй, B кoтopoм пoлyчAютcя peшeния для плAcтнчнocти, пpимeняя Bpeмя кAк изoбpeтeниe B AнAлизe BязкoплAcтичнocти, пoкA дocтигAютcя cocтoяния pABнoBecия для кAждoгo нocтyпAтeльнoгo ypoBня нAгpyзкн. ПpeдcтABляeтcя пoдpoбнoe нccлeдoBAниe нeлннeйнoгo пoBeдeния тopocфepичecкoгo cocyдA дABлeння, c цeлью иллюcтpAции эффeктиBнocти чиcлeнныч мeтoдoB.
    International Journal of Solids and Structures 01/1975; · 2.04 Impact Factor
  • S. Nagarajan, E.P. Popov
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    ABSTRACT: This paper presents an application of isoparametric elements for the elastic-plastic dynamic analysis of shells of revolution. General isoparametric elements with curved sides are used in the finiic element discretization. These are capable of representing solids of revolution in the form of a layered system. Structures with complex geometries and sharp discontinuities may be studied. Solutions can be obtained for both thin and thick shells because the customary Kirchhoff-Love hypothesis is not invoked.Dynamic analysis is carried out by means of step-by-step integration, the program allowing for the use of any of the schemes belonging to the Newmark family of methods (with free parameters γ and β) and the Wilson and Farhoomand θ-method. Flow theory of plasticity is used in the inelastic range and either isotropic hardening or kinematic linear hardening may be adopted. The program can analyze axisymmetric structures subjected To axially symmetric loading as well as plane stress problems. Numerical examples presented include the dynamic analyses of a simply supported beam and two spherical caps.
    Computers & Structures. 01/1974;
  • S. Nagarajan, E.P. Popov