Method and software for finite element solution of two-dimensional creep problems at large deformations

The paper presents the formulation of a two-dimensional problem of the creep theory for the case of finite strains. A description of the foundations of the calculation method presents. The method is based on the use of the generalized Lagrange-Euler (ALE) approach, in which the boundary value problem in the current solid configuration is solved by using FEM. A triangular element is involved in the numerical modeling. At each stage of creep calculations in the current configuration, the initial problem is solved numerically using the finite difference method. The preprocessing data preparation is carried out in the homemade RD program, in which two-dimensional model is surrounded by a mesh of special elements. This feature implements the ALE algorithm for the motion of material elements along the model. The examples of preprocessing as well as of the mesh rebuilding in the case of finite elements transition are given. Creep calculations are performed in the developed program, which is based on the use of the FEM Creep software package in the case of finite strains. The regular mesh is used for calculations, which allow us to use the efficient algorithm for transition between current configurations. The numerical results of the creep of specimens made from aluminum alloys are compared with the experimental and calculated ones obtained by integrating the constitutive equations. It was concluded that for material with ductile type of fracture the presented method and software allow to obtain results very close to experimental only by use of creep rate equation. Creep simulations of material with mixed brittle-ductile fracture type demand use the additional equation for damage variable.

Rotation-Free Based Numerical Model for Nonlinear Analysis of Thin Shells

This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi-Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.

Nonlinear Deformation and Numerical Post-Buckling Analysis of Plate Structures Using the Assumed Natural Strain Concept

In this study, an efficient triangular element for the fast nonlinear analysis of moderately thick Mindlin–Reissner plates is proposed. The element is formulated using a newly developed method, which is based on the assumed natural strain concept, and called Continuously Variable Strain (CVS). The continuous higher-order strain field is proposed by using the fundamental lemma of the variational calculus. Furthermore, the updated Lagrangian tensor together with rigid body terms is employed allowing for large deformations. The proposed element (CVST10), which is obtained by minimizing the total potential energy, has only 10 degrees of freedom and demonstrates high-efficiency and fast convergence rate in analysis of problems with coarse and distorted meshes. The arc-length iterative technique is applied to handle the geometrically post-buckling behavior of homogeneous plates under various load and boundary conditions. Various numerical examples prove the accuracy of the proposed element.

A 4-node quadrilateral element with center-point based discrete shear gap (CP-DSG4)

This work aims at presenting a novel four-node quadrilateral element, which is enhanced by integrating with discrete shear gap (DSG), for analysis of Reissner-Mindlin plates. In contrast to previous studies that are mainly based on three-node triangular elements, here we, for the first time, extend the DSG to four-node quadrilateral elements. We further integrate the fictitious point located at the center of element into the present formulation to eliminate the so-called anisotropy, leading to a simplified and efficient calculation of DSG, and that enhancement results in a novel approach named as "four-node quadrilateral element with center-point based discrete shear gap - CP-DSG4". The accuracy and efficiency of the CP-DSG4 are demonstrated through our numerical experiment, and its computed results are validated against those derived from the three-node triangular element using DSG, and other existing reference solutions.

Static Analysis of Stiffened Shells Using an Edge-Based Smoothed MITC3 (ES-MITC3) Method

A novel approach for solving the stiffened shell structures by using an edge-based smoothed MITC3 finite element method (ES-MITC3) is presented in this paper. The ES-MITC3 method is an efficient finite element method by combining the edge-based smoothed finite element method (ES-FEM) with the original MITC3 triangular element to not only significantly improve the accuracy but also overcome the shear-locking phenomenon in the Reissner–Mindlin shell analysis. In this study, the ES-MITC3 method is applied for shell structures and then reinforced by stiffeners based on the Timoshenko beam theory to achieve more durability and strength structures. The transverse displacements of the shell structures and stiffeners at the contact positions are assumed compatible. Numerical results of the ES-MITC3 element are compared with those of available other numerical results to demonstrate a good convergence and accuracy of the present method.

The family of multilayered finite elements for the analysis of plates and shells of variable thickness

Urban development requires careful attitude to environment on the one hand and protection of the population from the natural phenomena on the other. To solve these problems, various building structures are used, in which slabs and shells of variable thickness find the wide application. In this work, the family of multilayered finite elements for the analysis of plates and shells of variable thickness is described. The family is based on the simplest flat triangular element of the Kirchhoff type. The lateral displacements in this element are approximated by an incomplete cubic polynomial. Such an element is unsuitable for practical use, but on its basis, improved elements of triangular and quadrilateral shape are built. Particular attention is paid to taking into account the variability of the cross-section. The results of the developed elements testing are presented, and the advantages of their use in the practice of designing and calculating the structures are shown. El desarrollo urbano requiere una actitud cuidadosa con el medio ambiente, por un lado, y la protección de la población frente a los fenómenos naturales, por otro. Para resolver estos problemas, se utilizan diversas estructuras de edificios, en las que las placas y cáscaras de espesor variable encuentran una amplia aplicación. En este trabajo se describe la familia de elementos finitos multicapa para el análisis de placas y cáscaras de espesor variable. La familia se basa en el elemento triangular plano más simple del tipo Kirchhoff. Los desplazamientos laterales en este elemento se aproximan mediante un polinomio cúbico incompleto. Este elemento es inadecuado para su uso práctico, pero sobre su base se construyen elementos mejorados de forma triangular y cuadrilátera. Se presta especial atención a tener en cuenta la variabilidad de la sección transversal. Se presentan los resultados de las pruebas de los elementos desarrollados y se muestran las ventajas de su uso en la práctica del diseño y el cálculo de las estructuras.

An edge-based smoothed finite element for buckling analysis of functionally graded material variable-thickness plates

The paper aims to extend the ES-MITC3 element, which is an integration of the edge-based smoothed finite element method (ES-FEM) with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3 element), for the buckling analysis of the FGM variable-thickness plates subjected to mechanical loads. The proposed ES-MITC3 element is performed to eliminate the shear locking phenomenon and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing the same edge. The numerical results demonstrated that the proposed method is reliable and more accurate than some other published solutions in the literature. The influences of some geometric parameters, material properties on the stability of FGM variable-thickness plates are examined in detail.

A Triangular Plate Bending Element Based on Discrete Kirchhoff Theory with Simple Explicit Expression

A Simple three-node Discrete Kirchhoff Triangular (SDKT) plate bending element is proposed in this study to overcome some inherent difficulties and provide efficient and dependable solutions in engineering practice for thin plate structure analyses. Different from the popular DKT (Discrete Kirchhoff Theory) triangular element, using the compatible trial function for the transverse displacement along the element sides, the construction of the present SDKT element is based on a specially designed trial function for the transverse displacement over the element, which satisfies interpolation conditions for the transverse displacements and the rotations at the three corner nodes. Numerical investigations of thin plate structures were conducted, using the proposed SDKT element. The results were compared with those by other prevalent plate elements, including the analytical solutions. It was shown that the present element has the simplest explicit expression of the nine-DOF (Degree of Freedom) triangular plate bending elements currently available that can pass the patch test. The numerical examples indicate that the present element has a good convergence rate and possesses high precision.

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.

Optimization of diagrid geometry based on the desirability function approach

Diagrids represent one of the emerging structural systems employed worldwide for the construction of high-rise buildings. Their potential relies on the peculiar architectural effect and their great lateral stiffness. Because of the modular nature of the diagrid triangular element, optimization processes are usually carried out to assess the best arrangement of the external diagonals in order to enhance the structural performance while using the lowest amount of structural material. In this contribution, we make use for the first time of the desirability function approach to investigate the optimal geometry of the dia-grid system. A 168-meter tall building, with four different floor shapes, is analyzed, and the inclination of the external diagonals is varied between 35° and 84°. The desirability function approach is applied to find the most desirable geometry to limit both the lateral and torsional deformability, the amount of employed material as well as the construction complexity of the building. A sensitivity analysis is also carried out to investigate the influence of the individual desirability weight on the obtained optimal geometry. The effect of the building height is finally evaluated, through the investigation of sets of 124-, 210- and 252-meter tall diagrid structures.