Element Formulation For Nonlinear Analysis Research Articles

Bubble-enhanced quadrilateral finite element formulation for nonlinear analysis of geotechnical problems

We investigate a new numerical procedure based on a bubble-enriched finite element formulation in combination with the implicit backward Euler scheme for nonlinear analysis of strip footings and stability of slopes. The soil body is modeled as a perfect plastic Mohr–Coulomb material. The displacement field is approximated by a 4-node quadrilateral element discretization enhanced with bubble modes. Collapse loads and failure mechanisms in cohesive frictional soil are determined by solving a few Newton–Raphson iterations. Numerical results of the present approach are verified by both analytical solutions and other numerical solutions available in the literature.

An efficient finite element formulation for nonlinear analysis of clustered tensegrity

Purpose– The purpose of this paper is to propose an efficient finite element formulation for nonlinear analysis of clustered tensegrity that consists of classical cables, clustered cables and bars.Design/methodology/approach– The derivation of the finite element formulation is based on the co-rotational approach, which decomposes a geometrically nonlinear deformation into a large rigid body motion and a small-strain deformation. A tangent stiffness matrix of a clustered cable is proposed and the Newton-Raphson scheme is employed to solve the nonlinear equation.Findings– The derived tangent stiffness matrix, including an additional stiffness terms that describes the slide effect of pulleys, can regress to the stiffness matrix of a classical cable, which is convenient for the implementation of finite element procedure. Two typical numerical examples show that the proposed formulation is accurate and requires less iteration than the force density method.Originality/value– The co-rotational formulation of a clustered cable is originally proposed, although some mature methods, such as the TL, Force Density and Dynamic Relaxation method, have been applied to nonlinear analysis of clustered tensegrity. The proposed co-rotational formulation proved efficient.

A 6DOF super element for nonlinear analysis of composite frames with partial interaction and semi-rigid connections

This paper presents a displacement-based finite element formulation for nonlinear analysis of steel - concrete composite planar frames subjected to combined action of gravity and lateral loads. A 6DOF super element is proposed for modeling composite beam, allowing for partial interaction between the steel beam and the concrete slab, semi-rigid nature of beam to column composite connection and material nonlinearity. The load control method and the displacement control method are utilized for tracing the structural equilibrium paths, and the direct method is utilized for solving the nonlinear problem. Numerical examples, concerning a two-span continuous composite beam, a portal composite frame and a six-storey composite frame, are performed. The results are compared with experience data or theoretical results from other studies and are discussed for influences of the factors mentioned above on behaviour of composite beams and composite frames.

Finite Element formulation for nonlinear analysis of masonry walls

The work builds upon previous developments made by the authors in the context of the nonlinear, in-plane analysis of masonry walls. The structural behavior is characterized by phenomena, such as strain localization, damage, and friction, which need to be modeled at fine scales. Fine-scale modeling represents a significant challenge with regards to numerical simulations, due to its computational expensiveness and hard manageability. Generally, it requires sophisticated solution strategies, such as multi-grid techniques, as proposed in 2007 by the same authors, which cannot be effortlessly used in engineering softwares for structural analysis and design. In order to overcome such difficulties, we propose a coarse-scale model, to be employed in standard path-following techniques, based on an assumed stress Finite Element formulation in a context of non-associated plasticity. We obtain the nonlinear behavior by assuming a set of planes on the Element where frictional response can take place, together with tensile and compression limit stress. In this way, we capture the essential features of the nonlinear behavior as described by the more refined models developed in the past, exploiting algorithms widely adopted in elasto-plasticity, and therefore suitable for practical use in the analysis of full scale masonry structures.

NONLINEAR STABILITY ANALYSIS OF THIN-WALLED FRAMES USING UL–ESA FORMULATION

This work presents a one-dimensional finite element formulation for nonlinear analysis of spaced framed structures with thin-walled cross-sections. Within the framework of updated Lagrangian formulation, the nonlinear displacement field of thin-walled cross-sections, which accounts for restrained warping as well as the second-order displacement terms due to large rotations, the equations of equilibrium are firstly derived for a straight beam element. Due to the nonlinear displacement field, the geometric potential of semitangential moment is obtained for both the torsion and bending moments. In such a way, the joint moment equilibrium conditions of adjacent non-collinear elements are ensured. Force recovering is performed according to the external stiffness approach. Material nonlinearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends and for this a corresponding plastic reduction matrix is determined. The interaction of element forces at the hinge and the possibility of elastic unloading are taken into account. The effectiveness of the numerical algorithm discussed is validated through the test problem.

A mixed finite element formulation for non-linear analysis of plane problems

Based on the incremental non-linear theory of solid bodies and the Hellinger-Reissncr principle, a mixed updated Lagrangian formulation of the large displacement motion of solid bodies is derived, and an associated mixed finite element model is developed. The model contains the displacements and stresses as the nodal degrees of freedom. The model is used for the large deformation elasto-plastic analysis of plane problems. In solving non-linear problems, the Newton-Raphson method with arc-length control is adopted to trace the post-buckling response. The computational steps to calculate the elasto-plastic stress increments at Gauss points in the elasto-plastic analysis by the present mixed model are described in detail. Numerical results are presented and compared with those of the displacement model and existing solutions to show the accuracy of the present mixed model in the large deformation elasto-plastic analysis of plane problems.

A multi-director formulation for nonlinear elastic-viscoelastic layered shells

A C 0 finite element formulation for nonlinear analysis of multi-layered shells comprised of elastic and viscoelastic layers is presented for applications involving small strains but finite rotations. The elastic and viscoelastic layers may occupy arbitrary layer locations and the formulation is applicable to thick and thin shells. The formulation utilizes a three-dimensional variational approach in which the layered shell is represented as a multi-director field. The incorporated kinematic theory describes, within individual layers, the effects of transverse shear and transverse normal strain to arbitrary orders in the layer thickness coordinate. Stresses are computed through the three-dimensional constitutive equations and the usual “zero normal stress” shell hypothesis is not employed. Sufficiently general constitutive equations for the viscoelastic layers are proposed in objective rate form and a product algorithm, based on an operator split in the complete set of constitutive equations, is used for the temporal integration of the rate equations. The definition of the tangent operator, used in Newton's method for the solution of the nonlinear equations, is derived consistently from the product algorithm. Observations on the use of reduced/selective integration in the presence of high order kinematics are made and a number of numerical examples are presented to illustrate the capability of the formulation.

New design method of permanent magnets by using the finite element method

A new method for determining the shapes and sizes of magnets which produce the prescribed flux densities by using the finite element method has been developed. In this paper, the new technique is explained briefly, and then the finite element formulation for non-linear analysis is derived. Finally, the usefulness of the technique is shown by applying this method to the design of magnetic circuits.