Enhanced Rotation-Free Basic Shell Triangle. Applications to Sheet Metal Forming

Purpose – The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures. Design/methodology/approach – In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF). Findings – In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQUS finite element (FE) commercial software, show its good accuracy and robustness. Practical implications – An additional application including a multilayered composite structure and involving buckling and delamination was investigated using the present improved SPH model and the results are compared to the FE results, they confirmed both the efficiency and the accuracy of the proposed method. Originality/value – An efficient 2D-continuum SPH model for the geometrically nonlinear analysis of thin and thick structures is proposed. Contrarily to the classical SPH approaches, here the constitutive material relations are used to link naturally the stresses and strains. The Total Lagrangian approach is investigated to alleviate the tensile instabilities problem, allowing at the same time to avoid the updating procedure of the neighboring particles search and therefore reducing CPU usage. The proposed approach is valid for isotropic and multilayered composites structures undergoing large transformations. CPU time savings and better results with the new 2D-continuum SPH formulation compared to the classical continuum SPH. The explicit dynamic scheme was used for time integration allowing a fast resolution algorithm even for highly nonlinear problems.

The aim of this paper is to estimate the displacement and strain of a thin plane based on the 3- and 6- node triangular element using MATLAB. Firstly, MATLAB programming was applied to determine the stiffness matrix of 3- and 6-node triangular element in a two-dimensional plane. Secondly, MATLAB was continuous utilized to calculated strain and displacement of the plate when under tension condition based on both element types, also ANSYS software was employed to verify results obtained from MATLAB. Through the comparison of the two results, the error nearly zero, indicating the validation of MATLAB program. Eventually, the influence of the varying both elastic modulus and load on strain and displacement of the plate were analyzed. Results show that with the increase value of elastic modulus, the strain and displacement of both types of elements are all reduced. With the change of loading conditions, the corresponding displacement and strain conditions become complicated. In addition, quadratic triangular element provides more information than linear triangular element.

A new strain smoothing method for triangular and tetrahedral finite elements

In this paper, a novel enriched three-node triangular element with the augmented interpolation cover functions is proposed based on the original linear triangular element for two-dimensional solids. In this enriched triangular element, the augmented interpolation cover functions are employed to enrich the original standard linear shape functions over element patches. As a result, the original linear approximation space can be effectively enriched without adding extra nodes. To eliminate the linear dependence issue of the present method, an effective scheme is used to make the system matrices of the numerical model completely positive-definite. Through several typical numerical examples, the abilities of the present enriched three node triangular element in forced and free vibration analysis of two-dimensional solids are studied. The results show that, compared with the original linear triangular element, the present element can not only provide more accurate numerical results, but also have higher computational efficiency and convergence rate.

Synthetic division based integration of rational functions of bivariate polynomial numerators with linear denominators over a unit triangle {0⩽ ξ, η⩽1, ξ+ η⩽1} in the local parametric space ( ξ, η)

Several explicit schemes are presented for triangular P0 and P1 finite elements. A first‐order accurate upwind P0 scheme is compared to a FLIC type method. A second‐order accurate Richtmyer scheme is constructed. Applications are given for the Euler system of conservation laws in the 2‐dimensional case.

The finite element method capable of simulating the behavior of deep foundations subjected to negative skin friction in Basrah soil is investigated. Single piles under drag forces are analyzed using the PLAXIS program with an axisymmetric model. Linear elastic, Soft Soil and Mohr-Coulomb constitutive relations are adopted, where higher order triangular element is chosen for pile and soil clusters. Both pile and soil are modeled using (15)-node triangular elements. Three sites in Basrah province (Umm Qasr Port, Khor Al-Zubair, and Shatt AlArab Hotel) were selected to perform this study. The soil profile and layer characteristics are obtained from the soil investigation reports. Where the negative skin friction is evaluated due to filling loads. It is Conclusion thatSmall relative displacements are necessary to activate the negative skin friction. The elastic shorting for pile effect negative skin friction, due to increase relative displacement. The elastic shorting of the driven pile is more than that of the bored pile due to the less cross-sectional area of the driven pile. The results revealed proportional relation between the developed drag forces and pile section dimensions, interface friction factor, and fill height, with a maximum effect on the section dimension and minimum effect on the interface factor. The locations of neutral points are not sensitive to the above-mentioned factors.

On a robust FE2 model for delamination analysis in composite structures

A nonconforming eight to 26-node hexahedron for three-dimensional thermal-elasto-plastic finite element analysis

Adaptive triangular element generation and optimization-based smoothing, Part 1: On the plane

In the formulation of flat shell elements it is difficult to achieve inter-element compatibility between membrane and transverse displacements for non-coplanar elements. Many elements lack proper nodal degrees of freedom to model intersections making the assembly of elements troublesome. A flat triangular shell element is established by a combination of a new plate bending element DKTL and the well-known linear membrane strain element LST, and for this element the above-mentioned deficiencies are avoided. The plate bending element DKTL is based on Discrete Kirchhoff Theory and Loof nodes. The nodal configuration of the element is similar to the SemiLoof element, and the formulation is an improvement of a previous formulation. The element is used for both linear statics, linear buckling and geometrical non-linear analysis, and numerical examples are presented to show the robustness, accuracy and quick convergence of the element.

Shear and membrane locking-free two- and three-noded thin-walled curved beam elements with nonsymmetric cross-section are developed based on the assumed strain fields. The two-noded element is formulated from constant strain fields and three-noded one is from linear strain fields. Both elements consider extensional and inextensional conditions, respectively, along the centroid axis of beam. Since strain functions are assumed independently, proposed both elements are perfectly free from any locking phenomena and especially give explicit stress expression at an arbitrary point of cross-sections of curved beam. In order to illustrate the validity and the practical usefulness of the present assumed strain curved beam elements, the displacements and the normal stresses of curved arch with double-, mono-, and nonsymmetric cross-sections and the horizontally curved box girder with nonsymmetric cross-section are evaluated and compared with the analytical solutions, results from shell elements, and the experimental test results. The emphasis is given in investigating the influence of inextensibility along the beam axis on the behavior of curved beam with respect to the subtended angle, the slenderness ratio, and the boundary condition.

In order to improve the efficiency and stability of automobile hood doors under axial loading circumstances, this research investigates the reinforcing of these doors using graphene oxide powders (GOP). This work is separated into two different parts. In the first part, using the mathematical modeling, the results of the presented applicable structure are obtained. After that using the datasets of the mathematical modeling section, the results of deep neural networks (DNN) are trained, tested, and validated. The work focuses on double-curved panels’ linear strain fields, which are an essential part of vehicle construction. We solve the governing equations and boundary conditions for the reinforced automobile hood doors by using Navier’s solutions. GOP greatly enhances the mechanical characteristics by offering better load-carrying capability and deformation resistance. Our results show that DNNs can reliably and effectively forecast the performance of GOP-reinforced structures, providing a useful tool for improving automobile hood door designs. Enhanced automobile safety and durability are made possible by the combination of cutting-edge computational methodologies and novel materials, which also meet the increasing need for high-performance car components. This work highlights the revolutionary power of both technologies on contemporary vehicle design and manufacture, underscoring the mutually beneficial relationship between nanomaterial reinforcement and machine learning in the advancement of automotive engineering.

Use of lst elements in elastic-plastic solutions

Nonlinear analysis of FG-sandwich plates and shells