Nonlinear Analysis Of Thin-walled Structures Research Articles

A novel reduced-order method using mixed nonlinear kinematics for geometrically nonlinear analysis of thin-walled structures

Reduced-order methods based on the Koiter perturbation theory are applicable only to structural buckling problems, and high-order strain energy derivatives influence the computational efficiency of the methods. In this paper, a novel reduced-order method is proposed for the geometrically nonlinear analysis of thin-walled structures with large deflections. Mixed nonlinear kinematics are developed for the reduced-order method using co-rotational and updated von Kármán formulations. The co-rotational kinematics are applied to determine the internal force and tangent stiffness, whereas the third- and fourth-order strain energy derivatives are calculated using the updated von Kármán kinematics. Reduced-order models with one degree of freedom is constructed based on the perturbation theory, the solutions of which are nonlinear predictors of the geometrically nonlinear response. The use of mixed nonlinear kinematics significantly reduces the computational cost of constructing a reduced-order model. Nonlinear predictors are corrected using internal force-based residuals to ensure the accuracy of the geometrically nonlinear analysis. A geometrically nonlinear response with favorable smoothness is efficiently achieved using large step sizes in the path-following analysis. Various numerical examples, including the stiffened plate and wing structure, are provided to validate the accuracy and efficiency of the proposed method.

A corotational isogeometric assumed natural strain shell element in updated lagrangian formulation for general geometric nonlinear analysis of thin-walled structures

A new general geometric nonlinear curved quadrilateral shell element, which can handle large displacements and large rotations, is presented in this paper. It is formulated based on the incremental virtual work equation in updated Lagrangian formulation for general large displacement analysis. The kinematics of shell element is described using non-uniform B-spline patch, which results in the element displacement field with higher order continuity and the element performance more resistive to shear locking and membrane locking. In order to perfectly avoid such membrane locking and shear locking behaviors, the assumed in-plane membrane strain field and the assumed transverse shear strain field for the incremental covariant Green-Lagrange strain are constructed as linear combinations of non-uniform B-spline basis functions with degrees lower than those adopted by the original displacement field interpolation. In addition, based on Euler parameters, the corotational procedure available for high order isogeometric shell element is developed to extract the strain-producing deformational displacements and rotations and to update the element stresses and realistic internal force vectors. The accuracy and robustness of proposed shell element are demonstrated through the solutions of various benchmark problems.

Improved shell element for geometrically non-linear analysis of thin-walled structures

A six-node triangular shell element was developed to study the geometrically non-linear behaviour of open-section members. The present formulation is free from shear and membrane locking due to use of mixed interpolation of tensorial components scheme. Due to model thin-walled section, an improvement is considered to update the normal vectors of elements which are located at the angle between flange and web of section. In other words, an average of director vectors is employed for these elements in updating formulation. Moreover, the total Lagrangian formulation is employed to consider large displacement and rotation. An incremental iterative technique named generalised displacement control method is utilised to solve the governing equation. Several numerical examples are studied to illustrate the accuracy and predictability of the proposed formulation.

Geometrically nonlinear analysis of thin-walled structures using efficient Shell-based SPH method

Abstract In this paper a shell-based meshless formulation is proposed for the geometrically nonlinear analysis of thin-walled structures using an explicit dynamics scheme based on the Smoothed Particle Hydrodynamics (SPH) method. In the present investigation the SPH method is modified to deal with shell-like structures, while keeping its character of a strong formulation based on the principle of collocation directly applied on the differential equilibrium equations. The current SPH formulation is an extension of the continuum-improved and stabilized SPH method allowing a thin structure to be modeled using only one layer of particles to represent the shell mid-surface. Application of the present Shell-based SPH (SSPH) formulation for the analysis of several benchmarks including geometrically nonlinear behavior shows its validity and its potential especially in terms of CPU time saving while keeping a very good level of accuracy compared to the classical SPH method and to the Finite Element method.

A resultant 8-node solid-shell element for geometrically nonlinear analysis

A new resultant force formulation of 8-node solid element is presented for the linear and nonlinear analysis of thin-walled structures. The global, local and natural coordinate systems were used to accurately model the shell geometry. The assumed natural strain methods with plane stress concept were implemented to remove the various locking problems appearing in thin plates and shells. The correct warping behavior in the very thin twisted beam test was obtained by using an improved Jacobian transformation matrix. The 2 × 2 Gauss integration scheme was used for the calculation of the element stiffness matrix. From the computational viewpoint, the present solid element is very efficient for a large scale of nonlinear modeling. A lot of numerical tests were carried out for the validation of the present 8-node solid-shell element and the results are in good agreement with references.

Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability. Mechanical Engineering Series

Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability. Mechanical Engineering Series

Elastic and plastic analysis of thin-walled structures using improved hexahedral elements

In this paper a continuum based 3D-shell element for the nonlinear analysis of thin-walled structures is developed. Assumed natural strain method and enhanced assumed strain method are used to improve the relative poor element behaviour of a standard hexahedral displacement element. Different elastic and inelastic constitutive laws are considered. The anisotropic material behaviour of layered shells is modeled using a hyperelastic orthotropic material law in each layer. Furthermore, finite multiplicative J 2-plasticity is discussed. The models are characterized by an interface to the material setting of the boundary value problem. Several examples show the applicability and efficiency of the developed element formulation.

The geometric non-linear analysis of thin-walled structures by finite strips

The geometric non-linear analysis of prismatic thin-walled structures is presented. The theory is based on the moderately large displacement assumption, giving non-linear strain-displacement relations, but linear curvature-displacement relations. The corresponding non-linear equilibrium equations are produced by the principle of stationary potential energy using the finite strip discretisation. The equilibrium equations are solved using incremental and incremental-iterative numerical methods. Thus for the simple case of the square plate in edge compression, the self-correcting incremental method gives satisfactory results. For more complex examples of loading and structural type, a variable load incremental-iterative method is adopted. It is shown that the finite strip method used in conjunction with this method can be applied in particular to problems containing load maxima.