An unsymmetric 8-node hexahedral solid-shell element based on ANS and incompatible concepts for thin shell analysis

Reverse adjustment to patch test and two 8-node hexahedral elements

Fragile points method for Euler–Bernoulli beams

The finite volume method in the context of the finite element method

This study is focusing on the finite element simulation of low velocity impact applied to glass fiber-reinforced composites. Elasto-visco-plasticity is adopted taking into account strain rate effect, with isotropic hardening. To avoid numerical locking, hexahedral solid shell finite element SS is developed. The formulation is based on the mixed Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) methods. A geometrical non linear condition is applied. The finite element is implemented in UEL subroutine via the commercial software ABAQUS/Standard. The numerical element proved its efficiency comparing to conventional element and previous experimental results in (Mars et al. 2018). Numerical simulations with solid element are conducted using Abaqus/standard via user material UMAT subroutine. In terms of computation time, the solid shell element is less time consuming when comparing to conventional solid element. This is due to the fact that a single element through the thickness direction is adopted. Element efficiency is assessed for various fibers contents.

The paper deals with the validation of a recently proposed hexahedral solid-shell finite element in the buckling analysis of a laminated composite plate with delaminations. The object is to study the buckling behavior of structures with delaminations using the enhanced assumed strain (EAS) solid shell element with 5, 7 and 9 parameters. The EAS three-dimensional finite element formulation presented in this paper is free from shear locking and leads to accurate results for distorted element shapes. The developed FE model is used to study the effects of some parameters in the buckling load, such as the stacking sequences, delamination size, aspect ratio, width-to-thickness ratio. The feasibility of the proposed method is confirmed by numerical examples. Results show that using hexahedral solid-shell finite element in the buckling analysis is more efficient than using the enhanced solid finite element.

The classical 8-node isoparametric serendipity element uses parametric shape functions for both test and trial functions. Although this element performs well in general, it yields poor results under severe mesh distortions. The distortion sensitivity is caused by the lack of continuity and/or completeness of shape functions used for test and trial functions. A recent element using parametric and metric shape functions for constructing the test and trial functions exhibits distortion immunity. This paper discusses the choice of parametric or metric shape functions as the basis for test and/or trial functions, satisfaction of continuity and completeness requirements, and their connection to distortion sensitivity. Also, the performances of four types of elements, viz., parametric, metric, parametric-metric, and metric-parametric, are compared for distorted meshes, and their merits and demerits are discussed.

In the previous chapters, with an exception of GPG, the finite element formulations are based on the Galerkin methods in which test functions are chosen to be the same as the trial functions. This is not required in the weighted residual methods. Weighted residual methods other than the Galerkin methods include spectral element methods (SEM), least square methods (LSM), moment methods, or collocation methods, in which the test functions or weighting functions are not necessarily the same as the trial functions. In spectral element methods (SEM), polynomials in terms of nodal values of the variables are combined with special functions such as Chebyshev or Legendre polynomials. For least square methods, the test functions are constructed by the derivative of the residual with respect to the nodal values of the variables. Some arbitrary functions are chosen as test functions for the moment and collocation methods. Recently, the weighted residual concept has been used in meshless configurations, known as the finite point method (FPM), partition of unity method, meshless cloud method, or element-free method.

The main objective of this paper is to develop a numerical model susceptible to solve the numerical locking problems that may appear when applying the conventional solid and shell finite elements of ABAQUS. This model is based on a hexahedral solid shell element. The formulation of this element relays on the combination of the enhanced assumed strain (EAS) and assumed natural strain (ANS) methods with modified First Shear Deformation Theory (FSDT). The developed element is implemented into the ABAQUS user element (UEL) interface. The performance of this element is demonstrated by different benchmark tests from the literature. Our contribution consists on applying a single solid shell element through the thickness direction to predict the low velocity impact behavior on functionally graded material (FGM) circular plates.

In this paper, the structure of cylindrical shell with a reinforced circular cutout using combination model of solid element and shell element was analyzed by Finite Element Method (FEM) simulations. Multipoint constraint (MPC) method is mainly used to solve the connection between solid element and shell element when considering the calculation accuracy and efficiency of the model. The combination model of solid and shell element is established in ANSYS, and has been compared to the model of shell element and the model of solid element. The result showed that in the aspects of the stress distribution of the pressure hull near the cutout, buckling behavior of the structure and its instability response, the combination model of solid and shell element was almost equal to the others, it is convincible as well as possessing merits of other models.

An efficient multiphysics solid shell based finite element approach for modeling thin sheet metal forming processes

On the use of a reduced enhanced solid-shell (RESS) element for sheet forming simulations

Time periodic finite element solutions for sinusoidally excited electromagnetic field problems in moving media are presented. Solutions by the Galerkin method contain spurious oscillations when the grid Peclet number is more than one. To suppress these osillations an upwind finite element method using two different time periodic test functions is introduced. One is multiplied to second and first order space derivative terms and the other to the time derivative term. Test functions are obtained from trial functions by adding or subtracting quadratic bias functions with appropriate scaling factors. Phase differences are considered between trial functions and bias functions. For simple interpretations of the phase differences complex scaling factors are used. The proposed method is developed to give nodally exact solutions for uniform grid spacing in one dimensional problems. Based on the one dimensional results a two dimensional upwinding scheme is also derived.

A family of prismatic and hexahedral solid-shell (SHB) elements, with their linear and quadratic versions, is proposed in this work to model thin structures. The formulation of these SHB elements is extended to explicit dynamic analysis and large-strain anisotropic plasticity on the basis of a fully three-dimensional approach using an arbitrary number of integration points along the thickness direction. Several special treatments are applied to the SHB elements in order to avoid all locking phenomena and to guarantee the accuracy and efficiency of the simulations. These solid-shell elements have been implemented into ABAQUS standard/quasi-static and explicit/dynamic software packages. A number of static and dynamic benchmark problems, as well as a simulation of the deep drawing of a cylindrical cup, have been conducted to assess the performance of these SHB elements.

An eighteen-node, three-dimensional, solid element is presented for the finite element analysis of thin shell structures. The element is based on the Hellinger-Reissner principle with assumed independent strain divided into higher and lower order terms. The stiffness matrix associated with the higher order independent strain plays the role of a stabilization matrix. A modified stress-strain relation decoupling inplane and normal strain is used to incorporate thin shell behavior. Numerical results demonstrate that with a properly chosen set of assumed strain this element is effectively free of locking even for very thin plates and shells.

SummaryAmong all 3D 8‐node hexahedral solid elements in current finite element library, the ‘best’ one can produce good results for bending problems using coarse regular meshes. However, once the mesh is distorted, the accuracy will drop dramatically. And how to solve this problem is still a challenge that remains outstanding. This paper develops an 8‐node, 24‐DOF (three conventional DOFs per node) hexahedral element based on the virtual work principle, in which two different sets of displacement fields are employed simultaneously to formulate an unsymmetric element stiffness matrix. The first set simply utilizes the formulations of the traditional 8‐node trilinear isoparametric element, while the second set mainly employs the analytical trial functions in terms of 3D oblique coordinates (R, S, T). The resulting element, denoted by US‐ATFH8, contains no adjustable factor and can be used for both isotropic and anisotropic cases. Numerical examples show it can strictly pass both the first‐order (constant stress/strain) patch test and the second‐order patch test for pure bending, remove the volume locking, and provide the invariance for coordinate rotation. Especially, it is insensitive to various severe mesh distortions. Copyright © 2016 John Wiley & Sons, Ltd.