Elasto-plastic Analysis Of Shells Research Articles

Elastoplastic analysis of shells without any local iterative calculations by block Newton method

Elastoplastic analysis of shells without any local iterative calculations by block Newton method

Experimental study on low cycle fatigue strength of beam-to-column connections in steel bridge bents with different plate assembling and material mismatching

This study examined the effects of inherent defects due to plate assembling and material mismatched condition between base and weld metal on the fatigue strength of beam-to-column connections. Low cycle fatigue tests were carried out on specimens with different plate assembling systems and material mismatched conditions. The test results revealed that the global load-displacement relationships from specimens with different plate assembling systems and material mismatched conditions are similar, meaning these effects involve only local behavior of specimens. However, the fatigue strength of the specimens strongly depends on the location of defects resulting from plate assembling and mismatched conditions. The specimen with the undermatched conditions and the existing defect located closer to the corner of beam-to-column connection tends to have lower fatigue strength. The fracture surfaces indicated that failure patterns of specimen are different regarding mismatched conditions. While the crack propagated through the weld metal for the undermatched condition, it propagated towards the boundary between base and weld metal for overmatched condition. Elasto-plastic shell analysis was performed under the same condition as the experiments. And it is found that when evaluating fatigue strength of beam-to-column connections, the effects of plate assembling system and material mismatched condition should be considered.

Stress Resultant Based Elasto-Viscoplastic Thick Shell Model

The current paper presents enhancement introduced to the elasto-viscoplastic shell formulation, which serves as a theoretical base for the finite element code EPSA (Elasto-Plastic Shell Analysis) [1–3]. The shell equations used in EPSA are modified to account for transverse shear deformation, which is important in the analysis of thick plates and shells, as well as composite laminates. Transverse shear forces calculated from transverse shear strains are introduced into a rate-dependent yield function, which is similar to Iliushin's yield surface expressed in terms of stress resultants and stress couples [12]. The hardening rule defined by Bieniek and Funaro [4], which allows for representation of the Bauschinger effect on a moment-curvature plane, was previously adopted in EPSA and is used here in the same form. Viscoplastic strain rates are calculated, taking into account the transverse shears. Only non-layered shells are considered in this work.

Stress Resultant Based Elasto-Viscoplastic Thick Shell Model

The current paper presents enhancement introduced to the elasto-viscoplastic shell formulation, which serves as a theoretical base for the finite element code EPSA (Elasto-Plastic Shell Analysis) [1–3]. The shell equations used in EPSA are modified to account for transverse shear deformation, which is important in the analysis of thick plates and shells, as well as composite laminates. Transverse shear forces calculated from transverse shear strains are introduced into a rate-dependent yield function, which is similar to Iliushin's yield surface expressed in terms of stress resultants and stress couples [12]. The hardening rule defined by Bieniek and Funaro [4], which allows for representation of the Bauschinger effect on a moment-curvature plane, was previously adopted in EPSA and is used here in the same form. Viscoplastic strain rates are calculated, taking into account the transverse shears. Only non-layered shells are considered in this work.

Finite strain plasticity, the stress condition and a complete shell model

The null stress (s33 = 0) and incompressibility (J = 1) conditions in finite strain elasto-plastic shell analysis are studied in closed-form and implemented with a variant of the combined control by Ritto-Correa and Camotim. Coupling between constitutive laws and shell kinematics results from the satisfaction of either of the conditions; nonlocality results from the coupling. We prove that the conditions are, in general, incompatible. A new thickness-deformable is studied in terms of kinematics and strong-ellipticity. The affected continuum laws are derived and, in the discrete form, it is shown that thickness degrees-of-freedom and enhanced strains are avoided: a mixed displacement-shear strain shell element is used. Both hyperelastic and elasto-plastic constitutive laws are tested. Elasto-plasticity follows Lee’s decomposition and direct smoothing of the complementarity condition. A smooth root finder is employed to solve the resulting algebraic problem. Besides closed-form examples, numerical examples consisting of classical and newly proposed benchmarks are solved.

Anisotropic finite elastoplastic analysis of shells: simulation of earing in deep-drawing of single- and polycrystalline sheets by Taylor-type micro-to-macro transitions

The paper presents new aspects of anisotropic elastoplastic analyses of shells at finite strains. On the side of the computational shell analysis we design a surface-orientated brick-type mixed finite shell element in a setting relative to the parameter space of the shell equipped with shell-typical assumed strain modifications and an additive definition of an enhanced current metric in the Lagrangian representation. For this element we outline an interface to strain-driven constitutive stress update algorithms of multiplicative plasticity for single crystals and polycrystals at finite strains. On the side of computational plasticity we outline details of a constitutive model for finite single crystal plasticity. Here, we consider a distinct incremental variational formulation of the local constitutive elasto–visco-plastic response of single crystals in a multisurface format, where a quasi-hyperelastic stress potential is obtained from a local minimization problem with respect to the internal variables. It is shown that this local minimization problem determines the internal state of the material for finite increments of time. The proposed nonlinear shell formulation is applied to the simulation of earing in deep-drawing of anisotropic sheets. We present finite element simulations of cup-drawings of f.c.c. single crystal sheets and previously rolled polycrystalline f.c.c. sheets. The anisotropic polycrystal is modeled by a Taylor-type texture analysis based on an assumed microstructure of single crystal grains. A comparison with experiments underlines the performance of the simulation.

Elasto-plastic analysis of shells with the triangular element TRIC

TRIC is a simple but sophisticated three-node shear-deformable isotropic and composite facet shell element suitable for large-scale linear and nonlinear engineering computations of thin and moderately thick anisotropic plate and complex shell structures. In the present work an elasto-plastic constitutive model based on the von Mises yield criterion with isotropic hardening is incorporated into the element. The characteristic feature of this formulation is that the nonlinear material behaviour is taken into account entirely in the natural system of the element. This is achieved by transforming quantities such as equivalent plastic strain, equivalent stress, the expression of the yield surface and the components of flow vector from the material coordinate system to the natural coordinate system. These transformations lead to simple and elegant expressions for the respective quantities in the natural system which eventually result to an efficient and cost effective treatment of the nonlinear analysis of arbitrary shells including material and geometrical nonlinearities.

Constitutive model and finite element formulation for large strain elasto-plastic analysis of shells

This contribution presents a refined constitutive and finite element formulation for arbitrary shell structures undergoing large elasto-plastic deformations. An elasto-plastic material model is developed by using the multiplicative decomposition of the deformation gradient and by considering isotropic as well as kinematic hardening phenomena in general form. A plastic anisotropy induced by kinematic hardening is taken into account by modifying the flow direction. The elastic part of deformations is considered by the neo-Hookean type of a material model able to deal with large strains. For an accurate prediction of complex through-thickness stress distributions a multi-layer shell kinematics is used built on the basis of a six-parametric shell theory capable to deal with large strains as well as finite rotations. To avoid membrane locking in bending dominated cases as well as volume locking caused by material incompressibility in the full plastic range the displacement based finite element formulation is improved by means of the enhanced assumed strain concept. The capability of the algorithms proposed is demonstrated by various numerical examples involving large elasto-plastic strains, finite rotations and complex through-thickness stress distributions.

A theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains

The article presents new aspects of large-strain isotropic elastoplastic analysis of shells. On the shell theory side, we consider several possible continuum based parametrizations of the shell deformation and investigate their applicability with respect to the implementation of general three-dimensional local constitutive models. As an aspect of computational shell analysis we then discuss in detail the numerical implementation of a shell based on the parametrization of the top and bottom surface in terms of a new 8-node brick-type mixed finite shell element on the basis of assumed strain and enhanced strain variational approaches. On the side of plasticity theory we adopt a recently proposed intermediate-configuration-free formulation of large-strain plasticity based on the notion of a plastic metric and consider its representation with respect to the parameter manifold of the shell. This frame is formulated in terms of principal strains and principal stresses with respect to dual co- and contra-variant eigenvector triads associated with a mixed-variant elastic strain tensor. The new aspect of computational plasticity is the development of a stress update algorithm for the plasticity model mentioned above which includes a general return mapping in the eigenvalue space. The algorithm can be applied to general coordinate charts and is particularly convenient when formulated with respect to the space of the curvilinear coordinates of the shell parametrization. We demonstrate the performance of the finite element formulation and constitutive algorithms by means of several numerical examples.

An efficient formulation of integration algorithms for elastoplastic shell analysis based on layered finite element approach

For geometrically and physically nonlinear analyses of shell structures a computational model employing a Reissner-Mindlin type kinematic assumption, a layered finite element approach and a closest-point projection return mapping algorithm, completely formulated in tensor notation is presented. As a result of a consistent linearization, a tangent modulus is derived, expressed also in tensor components. The applied constitutive model includes a von Mises yield criterion and linear isotropic as well as kinematic hardening. All stress deviator components are employed in the formulation. The material model is implemented into a four-noded isoparametric assumed strain finite element, which permits the simulation of geometric nonlinear responses considering finite rotations. The proposed numerical concept is unconditionally stable and allows large time steps, as the numerical examples illustrate. Further, the numerical simulations demonstrate the expected quadratic convergence in a global iterative technique.

Nonlinear analysis of shells using the MITC formulation

The formulation of general shell elements using the method of mixed interpolation of tensorial components (MITC) is reviewed. In particular three elements that were formulated using the MITC method are examined: the MITC4 and MITC8 that were developed for general nonlinear analysis under the restriction of small strains and the MITC4-TLH that was developed for finite strain elasto-plastic analysis of shells.

Inelastic response of deeply submerged stiffened shells subjected to transient loads from explosions

The large deflection elastoplastic response of stiffened cylindrical shells subjected to transient loadings from explosions is considered. Because the cylinders are located at deep submergence, the effects of initial stress distributions due to hydrostatic pressure are included in the analysis. A large deflection elastoplastic shell theory is utilized in the analysis. This shell theory defines a yield surface at each cross section of the shell in terms of the moment and direct force components at the section. An associated flow rule is utilized to define the plastic‐strain rate. The EPSA (elastoplastic shell analysis) code is utilized in the analysis of the shell response to the dynamic loadings. Results obtained from the analysis have compared well with the results of experiments.

Large deflection elastoplastic analysis of thin shells

Results are presented and some modifications made to problems posed in an earlier paper by the authors on the extension of the semi-loof element to the analysis of shell structures involving instabilities, snap-through and material nonlinearities. In this paper, by adopting a more refined method for solving problems of plasticity, in conjunction with a subincremental technique, more accurate results are obtained. The second-order Runge-Kutta method employed in this study shows significant improvement in the accuracy of the streesses in the shell as compared to the case when only the simple point-slope method of Euler is used. The detailed computational procedure for elastoplastic analysis of shell problems is presented in a way that can readily be incorporated into standard computer packages. Results obtained for large deflection analysis of plastic shells of different geometries and boundary conditions are compared with the available solutions and show very good agreement.

Theory of Viscoplastic Shells for Dynamic Response

A viscoplastic shell model is formulated that utilizes the shell membrane strains and curvatures as the kinematic variables and the shell stress resultants (membrane forces and moments) as the dynamic variables. The viscoplastic shell model combines the concepts of Perzyna’s viscoplastic constitutive equations with Bieniek’s shell stress resultant formulation. The model is incorporated into the Elastoplastic Shell Analysis code (EPSA) for the analysis of shells in an acoustic medium subjected to dynamic loadings that produce moderately large elastoviscoplastic deformations in the shell. An example is presented to demonstrate the effect of material rate dependence on structural response.