Traditional Shell Elements Research Articles

Research on solid shell element based on penalty method

Since the angle degrees of freedom do not have the vector property, it is critical to handle this for nonlinear geometrical behavior. To simulate the nonlinear geometrical behavior of shell structure efficiently, we developed a solid‐shell element type without drilling degrees of freedom. In this paper, the element satisfies the assumption of the straight normal of the shell and we established penalty functions in the thickness direction of the shell. The formulations of equivalent node force and tangent stiffness obtained by 3D isoparametric element theory can be expressed by matrix forms clearly. The constitutive relationship in the global system is derived from the local constitutive matrix according to the tensor coordinate transform. Finally, taking a series of classic flat plate problems and curved shell problems as examples, the solid shell element using the penalty method is compared with the solid shell element using the artificial stiffness method and other shell elements. The results show that the solid element proposed in this paper can effectively eliminate shear self-locking after using the reduced integral scheme and obtain satisfactory accuracy for thin shells and medium-thickness•A type of solid shell element without rotational degrees of freedom is introduced using the penalty method.•A suitable penalty factor of this element is determined through numerical experiments.•This element is more efficient than the traditional shell elements and can be programmed with less time.

A new composite plate/plate element for stiffened plate structures via absolute nodal coordinate formulation

Two-dimensional plate/beam composite element is an effective method for deformation modeling of large thin-walled structure with stiffeners. However, the interface discontinuity is caused by the different stiffness of plate and beam structures, especially in the case of warping and torsional deformation, which reduces the calculation accuracy. In this paper, a composite plate/plate element model is proposed to describe the deformation of the stiffened plate structures. The plate element is developed via the absolute nodal coordinate formulation (ANCF) method and the slope of position is used to describe the rotation deformation, which releases the assumption of infinitesimal rotation in traditional shell element and may describe the large deformation problem. The consistent deformation conditions at contact interface between the plate and stiffener structures are deduced. Then, the mass, stiffness and generalized external force matrices of new plate/plate element are deduced. The static and dynamic analyses of the stiffened plate are conducted to verify the applicability of the new composite element, in which the cross-section size and the number of stiffeners are considered. The results show that the new plate/plate element may describe the mechanical behavior of stiffened plate structures and has a higher calculation accuracy than the common plate/beam elements.

Analysis of warping and distortion transmission in mixed shell\u2013GBT (generalized beam theory) models

Warping and distortion are relevant kinematic features of thin-walled beam structures, which have a non-trivial analysis. On this basis, this paper not only evaluates the possible kinematic transmissions involving high-order warping and distortion, but also presents a procedure to analyze structures using mixed models based on shell and Generalized Beam Theory (GBT) elements. In this mixed beam-shell structure, the traditional shell elements are applied at structural detailing points, such as joints, and GBT elements are used to model the beams/columns. Such a modeling technique uses the benefits of both elements. Shell elements can easily simulate different types of geometry conditions and details, such as stiffeners and holes; meanwhile, for the beams and columns, GBT can provide high performance, accuracy, and an easy modeling approach with clear results. The numerical formulation is based on multi-freedom constraint techniques. Special attention is given to the Master–Slave method, which is developed based on GBT kinematic assumptions. Furthermore, there is a discussion concerning the choice of the master degrees of freedom and its implications in numerical performance. An example of a thin-walled hollow circular cross section illustrates the proposed approach and is compared with fully shell element models.

Simulation of nonlinear benchmarks and sheet metal forming processes using linear and quadratic solid–shell elements combined with advanced anisotropic behavior models

A family of prismatic and hexahedral solid‒shell (SHB) elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact). Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.

A Modified Shell Element Model Combined with Yld91 Yield Function in Simulating Aluminum Alloy Applied Hydroforming

Hydroforming has been used widely across many industrial fields. Large applied pressure during hydroforming makes it necessary to consider the influence of normal stress in the thickness direction, while in FE simulation, the use of traditional shell element based upon plane-stress assumption is not appropriate in such cases. Here, the traditional shell element is modified by changing the constitutive relation which took into account the normal stress in the thickness direction, and the modified shell element formula is combined with Yld91 yield function to simulate the forming process of Aluminium alloy. Then the element formulation and material model is implemented into the FE code Ls-Dyna by means of USER interface. Two examples are carried out and good correlations are obtained when compared to the traditional shell element and solid element.

Simulating sheet metal double-sided hydroforming by using thick shell element

Double-sided hydroforming has been widely used in production since it can improve the formability and surface quality of sheet metals significantly. This paper investigates the application of thick shell element in finite element analysis of sheet metal forming process with pressure reacting on both sides of the blank. The computational efficiency and accuracy of thick shell element is compared with that of solid element and traditional shell element based on a numerical example. Then a double-sided blank hydroforming experiment is carried out to validate the thickness prediction ability of thick shell element, and the results show that the normal stress in the thickness direction caused by double-sided pressure reduces the material thickness and increases plastic strain and effective stress in the forming zone. Thick shell element, which can reflect the influence of normal stress on sheet metal forming process, is effective in finite element analysis of double-sided hydroforming.