E. P. Popov

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

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Publications (8)12.22 Total impact

  • 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; 11(1-11):1-19. DOI:10.1016/0020-7683(75)90099-2 · 2.04 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 01/1975; 9(3):535 - 550. DOI:10.1002/nme.1620090304 · 1.96 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 12/1974; DOI:10.1016/0045-7949(74)90028-5 · 2.18 Impact Factor
  • P.K. Larsen, E.P Popov
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    ABSTRACT: The incremental equilibrium equations for a body subjected to large deformations are given in a Lagrangian description. The loading terms due to both conservative and nonconservative types of loading are derived using virtual work considerations. The simple integral constitutive laws of the infinitesimal theory of linear viscoelasticity are generalized to small strain, large rotation applications through the use of invariant strain and stress measures. The viscoelastic material is characterized using a Prony series expansion for the relaxation modulus, leading to a simple algorithm for the evaluation of the convolution integrals. The shell geometry and displacement fields are discretized by the “degenerate” isoparametric shell element. The numerical examples include the post-buckling behavior of an elastic shallow spherical shell and the viscoelastic creep buckling of a spherical cap subjected to sustained loading.
    Computer Methods in Applied Mechanics and Engineering 03/1974; DOI:10.1016/0045-7825(74)90027-9 · 2.63 Impact Factor
  • P. K. Larsen, E. P. Popov
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    ABSTRACT: The derivation of incremental equilibrium equations from virtual work considerations is reviewed. The mathematical structure of these equations in the most common modes of description is discussed, and their feasibility for numerical applications is evaluated. The out-of-balance loading terms are included, and the effect of neglecting nonsymmetric stiffness terms originating from nonconservative loading is given. Then the use of exact and approximate constitutive laws for large inelastic deformation is discussed in the context of finite element applications. Emphasis is given to the various levels of approximations and assumptions in the latter type of relations and to their importance in the choice of mode of descriptions for problems with material and geometrical nonlinearities.Betrachtet wird die Herleitung von Gleichgewichtsbedingungen des Zuwachses aus virtuellen Arbeiten. Der mathematische Aufbau dieser Gleichungen in den gebruchlichsten Darstellungsarten und ihre Brauchbarkeit fr numerische Anwendungen wird diskutiert. Der Einflu der Vernachlssigung der durch nichtkonservative Belastung verursachten nichtsymmetrischen Steifigkeitselemente wird angegeben, und die nicht im Gleichgewicht befindlichen Belastungsanteile werden bercksichtigt. Anschlieend wird die Verwendung von Nherungen von Werkstoffgesetzen bei unelastischer Deformation im Hinblick auf die Verwendung in der methode der finiten Elemente diskutiert. Besondere Beachtung gilt den verschiedenen Nherungen und Annahmen in diesen Beziehungen und der Bedeutung der Wahl der Darstellungsart fr Probleme mit geometrischen und werkstoffbedingten Nichtlinearitten.
    Acta Mechanica 02/1974; 19(1):1-14. DOI:10.1007/BF01176266 · 1.47 Impact Factor
  • P. K. Larsen, E. P. Popov
  • 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 01/1974; 3(4):385 - 399. DOI:10.1002/eqe.4290030409 · 1.95 Impact Factor
  • S. Nagarajan, E.P. Popov