Arc-length Method Research Articles

Stability Analysis of Plate-Cone Reticulated Shell

This paper carries out stability analysis on plate-cone reticulated shell considering geometrical nonlinearity of cooperating work between plates and members. In this paper, stability behavior of different kinds of plate-cone reticulated shell considering geometrical nonlinearity is analyzed by using the software ANSYS, tracking complete process balance path for load-displacement by using arc-length method, the several problems of plate-cone reticulated shell are studied, such as destruction mechanism, structural ductility, ultimate bearing capacity and strength reserve, some important conclusions are obtained. After analyzing the stability behavior of double-layer reticulated shell by ANSYS and comparing with plate-cone reticulated shell, it is proved that plate-cone reticulated shell is more advantageous than double-layer reticulated shell in the aspect of stability behavior.

Nonlinear Stability Analysis on Vessels Subjected to External Pressure

To determine stability performance and the critical load of the short cylinder vessel which is made of steel, this paper carried out the finite element linear buckling analysis for 5 meters long steel pressure vessel and obtained buckling critical load. Then performed the nonlinear instability analysis by the arc-length method and obtained the load-displacement curves of the overall stability of the pressure vessel structure. The critical load can be got by twice the elastic slope method and double-tangent intersection method, and the loads are slightly higher than the result of the theoretical calculation, so the result of the theoretical calculation is safe and reliable. Finally, several measures keeping stability of short cylinder pressure vessel are proposed.

MODELING AND SIMULATION OF BUCKLING AND POSTBUCKLING OF PLANT STEMS UNDER COMBINED LOADING CONDITIONS

Numerical simulations for local buckling and postbuckling behavior of plant stems are presented under two combined loading cases: (1) axial compression (caused by axial grains) combined with wind pressure; and (2) bending moment (caused by eccentric axial grains) combined with wind pressure. Based on its microstructure, a hollow plant stem is modeled as a stringer stiffened multiwalled shell. The material properties of the stem are assumed to be orthotropic. The nonlinear governing equations for buckling and postbuckling of plant stems are solved through arc-length method along with Newton–Raphson technique. The numerical calculations are carried out using the finite element package ABAQUS. The results show that the postbuckling equilibrium path is unstable for plant stems subjected to axial compression or bending combined with relatively low values of wind pressure. Large reduction in buckling load and in postbuckling strength can be found even if the applied wind pressure is relatively small, which results in the easy occurrence of stem lodging.

Ultimate bearing capacity of concrete dam involved in geometric and material nonlinearity

To get the actual ultimate bearing capacity of concrete dam, the effect of geometric nonlinearity and strain softening on it, which appears in the failure process of concrete dam, is studied. Overload method is adopted to obtain the bearing capacity of a concrete dam by taking into consideration strain softening in the material constitutive law, geometric nonlinearity in geometric equation and equilibrium differential equation. Arc-length method is used to find the extreme point and descending branch of the load-displacement curve of the dam. The results present that the effect cannot be ignored. And geometric nonlinearity of structure and strain softening of materials should be considered for numerical analysis of ultimate bearing capacity of a concrete dam.

The possibility of a theoretical confirmation of the experimental values of the external critical pressure of thin-walled cylindrical shells

The problem of the buckling of elastic, isotropic, thin-walled cylindrical shells with small initial shape defects that are under the action of an external pressure is solved in a geometrically non-linear formulation. Equations that are identical to Marguerre's equations for a shallow cylindrical shell are used in formulating the problem. The solution is constructed by the Rayleigh–Ritz method with the points of the middle surface of the shell approximated by double functional sums over trigonometric and beam functions. The system of non-linear equations obtained is solved by arc-length methods. Cases of the clamped and supported shells when loading with a lateral and uniform hydrostatic pressure are considered. Its deflections from the limit points of the postbuckling branches of its loading trajectory are used as the initial imperfections. An inspection of the different forms of the initial imperfections when they have maximum values of up to 30% of the shell thickness made it possible to obtain practically the whole range of experimentally found critical pressures.

Nonlinear Stability Bearing Capacity Analysis for Plate-Cone Reticulated Shell

Plate-cone reticulated shell is a new type of double-layer reticulated shell in which ventral members is replaced by cone elements. This paper carries out nonlinear stability bearing capacity analysis on plate-cone reticulated shell considering geometrical nonlinearity of cooperating work between plates and members. In this paper, stability bearing capacity of plate-cone reticulated shells with different kinds of structure form considering geometrical nonlinearity is analyzed by using the software ANSYS, tracking complete process balance path for load-displacement by using arc-length method, the several problems of plate-cone reticulated shell are studied, such as destruction mechanism, structural ductility, stability ultimate bearing capacity and strength reserve, some important conclusions are obtained. After analyzing the stability behavior of double-layer reticulated shell by ANSYS and comparing with plate-cone reticulated shell, it is proved that plate-cone reticulated shell is more advantageous than double-layer reticulated shell in the aspect of stability bearing capacity behavior.

SGBEM for Cohesive Cracks in Homogeneous Media

In this paper, the Symmetric Galerkin Boundary Element Method for Linear Elastic Fracture Mechanics is extended to non-linear cohesive cracks propagating through homogeneous linear elastic isotropic media. The cohesive model adopted is based on the concept of free energy density per unit undeformed area. The corresponding constitutive cohesive equations present a softening branch which induces a potential instability. Thus, a suitable solution algorithm capable of following the growth of the cohesive zone is needed, and in the present work the numerical simulation is controlled by an arc-length method combined with a Newton-Raphson algorithm for the iterative solution of nonlinear equations. The Boundary ElementMethod is very attractive for modeling cohesive crack problems as all nonlinearities are located on the boundaries of linear elastic domains. Moreover a Galerkin approximation scheme, applied to a suitable symmetric boundary integral equation formulation, ensures an easy and efficient treatment of cracks in homogeneous media and an excellent convergence behavior of the numerical solution. The cohesive zone model is applied to simulate a pure mode I crack propagation in concrete. Numerical results for three-point bending test are used to check the numerical results for mode I and are compared with some numerical results obtained by FEM analysis found in the literature.

Local Buckling Analysis for Large Diameter Underground Jacked Steel Tubes under External Load

Densely arranged underground steel tube system (DAUSTS) is a new kind of structure which can be usually used in constructing spacious underground structures such as metro stations. During the construction, the steel tube is horizontally forced into soil by jacks through a vertical well. The tube may generate local buckling phenomena under the compression force if the parameter of the tube and soil meet the buckling condition. In the paper, the soil perturbation mode and the deformation of the tube before local buckling are both analyzed, considering the possibly concerned buckling failure modes in practical engineering, the confine effect of the soil and interaction between the tubes. A nonlinear buckling analysis on tube-wall of the steel tube located in the most unfavorable place is developed by the arc-length method of the finite element method (FEM), considering the effect of the large deformation. The results of the numerical simulation matches very well to the real application and the key results of the analysis can be used as an estimation principle for the stability of the tube.

An Improved Bubble Packing Method for Unstructured Grid Generation with Application to Computational Fluid Dynamics

An improved bubble packing method (BPM) is proposed to generate high-quality unstructured grids for prediction of the flow field in a domain with complex geometry. For a curved-boundary domain, bubble departure from the curved boundaries during the dynamic movement of bubbles can be avoided by using the mapping and the arc-length parameterization methods. Furthermore, the grid density of the whole region can be controlled effectively. Local mesh refinement is achieved by adding bubbles with different sizes to the real and artificial vertices of the domain, and vertex information is transferred to the inner nodes of the domain using the Shepard interpolation method. In order to validate the proposed BPM, a finite-volume solver on an unstructured collocated grid is developed to simulate both square and polar lid-driven cavity flows. The numerical simulation results agree well with the experimental data under different Reynolds numbers.

A simple explicit arc-length method using the dynamic relaxation method with kinetic damping

The explicit arc-length method is simulated to trace the post-buckling equilibrium path of structures by using dynamic relaxation method with kinetic damping. This method based on the cylindrical arc-length method does not require the computation and formulation of any tangent stiffness matrix to search the snap-through or snap-back problems. The convergence to the solution is achieved by using only vector equation with kinetic damping technique. Two approaches for cylindrical arc-length control are formulated with incremental and total displacement constraint. The merits of the explicit arc-length method, in tracing the post-buckling behavior of structures, are demonstrated by analyzing the numerical examples.

The Arc-Length Method from Controlling Load to Controlling Electric Potential

This paper generalizes the arc-length method, and proposes a new scheme of controlling equilibrium path including static equilibrium and electrostatic equilibrium. To take example for the thin plate electrode posing on the electrostatic field force, whose governing equations are the two fold nonlinear coupling equation, the method to compute the incremental factor is give in detain. The result is to show that not only the approximate critical voltage is obtained but also the trace after losing stability is found stably.

Post buckling analysis of shear deformable shallow shells by the boundary element method

AbstractThis paper presents four boundary element formulations for post buckling analysis of shear deformable shallow shells. The main differences between the formulations rely on the way non‐linear terms are treated and on the number of degrees of freedom in the domain. Boundary integral equations are obtained by coupling boundary element formulation of shear deformable plate and two‐dimensional plane stress elasticity. Four different sets of non‐linear integral equations are presented. Some domain integrals are treated directly with domain discretization whereas others are dealt indirectly with the dual reciprocity method. Each set of non‐linear boundary integral equations are solved using an incremental approach, where loads and prescribed boundary conditions are applied in small but finite increments. The resulting systems of equations are solved using a purely incremental technique and the Newton–Raphson technique with the Arc length method. Finally, the effect of imperfections (obtained from a linear buckling analysis) on the post‐buckling behaviour of axially compressed shallow shells is investigated. Results of several benchmark examples are compared with the published work and good agreement is obtained. Copyright © 2010 John Wiley & Sons, Ltd.

On the analysis of simple shear problem using the micro-polar hypoelasticity Cosserat theory

In this paper, an analysis of kinematics of the isotropic elastic Cosserat continuum is presented in infinitesimal and finite deformations. Emphasis is given on the applicability of corotational stress rates for hypoelasticity in micro-polar continua. A non-linear finite element analysis is performed with an explicit formulation of tangent stiffness matrices in the case of Truesdell stress and couple stress rates. A comprehensive path-dependent procedure is employed based on the arc-length method to calculate the stability points and handle the snap-back problem. Finally, the accuracy and efficiency of method are illustrated by numerical examples.

Computational analysis of progressive failure in a notched laminate including shear nonlinearity and fiber failure

A computational model for mesolevel analysis of progressive laminate failure is presented. A previously developed discrete model for mesh independent representation of matrix cracks is combined with continuum descriptions for fiber failure and matrix nonlinearity. For fiber failure, a continuum damage model is introduced and a phenomenological damage/plasticity law is used for the shear nonlinearity. Special attention is paid to the application of the dissipation based arclength method to these models, where the presence of residual stresses is also taken into account. With the analysis of a notched cross-ply laminate the importance of the different components of the model to capture the complete failure process correctly is exemplified.

Nonlinear static and dynamic analysis of shells of revolution

In this study, geometrically nonlinear static and dynamic response of shells of revolution is investigated using an isoparametric axisymmetric shell element. The formulation is based on the total Lagrangian approach and the material behavior is assumed to be linearly elastic. The Arclength method is used to analyze the post-buckling behavior and the Newmark’s integration technique coupled with the Newton–Raphson iteration scheme is employed for dynamic responses. Various numerical examples are performed to obtain the geometrically nonlinear static and dynamic behavior of shells of revolution subjected to step loads.

Computation of invariant manifolds with self-adaptive parameter and trajectories continuation method

Most work on manifold study focuses on two-dimensional manifolds and there have been proposed some good computing methods. However, the computation of two-dimensional manifold is still a hot research field. In this paper the two-dimensional manifold of hyperbolic equilibria for vector fields is computed by combining self-adaptive parameter with trajectories continuation, approximating the local manifold with an ellipse around the equilibria, extending the trajectory with equal distance, and adjusting the trajectory with self-adaptive parameter. This method is more accurate than the "trajectories and arc-length method", and better shows the trend of the manifolds than the "box covering method".

Numerical analysis of the effect of torispherical head on the buckling of pressure vessels

Effect of torispherical head on the buckling of pressure vessels was investigated by finite element (FE) method. The FE method with use of nonlinear buckling analysis was applied to predict the critical buckling Load. The influences of geometrical parameter such as thickness, knuckle radius and diameter of cylindrical part, on the buckling of heads have been studied. The Arc Length method which can control the load level, the length of the displacement increment and the maximum displacement was been used. By verification performed with the European Convention for Constructional Steelwork (ECCS) code, it was confirmed that the nonlinear buckling analysis could assure accurate results for buckling strength. It was shown that geometrical imperfections had little effect on buckling strength.

Vibration characteristics and snapping behavior of hygro-thermo-elastic composite doubly curved shells

Abstract Due to the change in environmental conditions, hygrothermal residual stresses may induce buckling and dynamic instability in composite shell structures. This paper investigates the vibration characteristics of pre- and post-buckled hygro-thermo-elastic laminated composite doubly curved shells. The geometrically nonlinear finite element method is used for the analysis. Both deep and shallow shell surfaces are modeled using an orthogonal curvilinear coordinate system. The mechanical linear, nonlinear stiffnesses, the hygrothermal nonlinear geometric stiffness and the hygrothermal load vector are presented. The arc-length method is implemented to capture the snapping behavior of the structures under hygrothermal environmental conditions. Numerical results of nonlinear deflections and fundamental frequencies along with the deflection shapes and the mode shapes are presented and discussed for spherical and cylindrical shell panels. The fundamental frequency decreases in the pre-buckling region and increases in the post-buckling domain of the snap-through process. It is also noted that as the thickness of the panel decreases, the limit point load for buckling decreases; if the radius of curvature increases, the fundamental frequency decreases under a uniform hygral condition. The “curve veering phenomena” is observed for spherical panel under thermal load. The geometrically nonlinear deflection behavior affects the vibration characteristics in a hygrothermal environment.

Nonlinear flutter of aerothermally buckled composite shells with damping treatments

Finite element analyses of the aerothermoelastic behavior of aerothermally buckled cylindrical composite shells with various damping treatments were implemented using the theory of layerwise displacement field. The arc-length method and iterative nonlinear scheme were taken up to estimate the post-buckling deformation of composite shells due to aerothermal loads. The complex modulus was adopted to take into account the effects of viscoelastic damping. The post-buckling behaviors and aeroelastic characteristics, under thermal loads, of several damped composite shells were investigated with various damping treatments including free layer and constrained layer and sandwiched damping layers. The results show that the flutter boundary of the cylindrical composite panels with viscoelastic layers can be remarkably affected by the aerothermally buckled shapes and damping treatments. Further, the proper damping treatments, coupled with thermal loads, can improve aerothermoelastic characteristics, resulting in the increase of the flutter boundary.

Thermal post-buckled behaviors of cylindrical composite shells with viscoelastic damping treatments

The finite element method for the vibration and damping analyses of the thermal post-buckled cylindrical composite shells with damping treatments was developed adopting the layerwise displacement field theory. The arc-length method was used to trace the nonlinear post-buckling behavior of the composite shell induced by the thermal load, and the complex modulus was adopted to consider the effects of the structural damping. The verification of the present results was performed in comparison with previous results, and the dynamic characteristics of several composite shells with damping treatments were investigated. The results show that the viscoelastic damping treatments could significantly affect the thermal post-buckling behaviors and the dynamic characteristics of the composite shells.