Geometrical nonlinear analysis based on optimization technique

This paper provides information on hyperboloids of revolution surfaces and their classification, using methods of differential geometry and computer design. All surfaces are plotted by means of computer graphics. The geometric nonlinear numerical analysis of thin shells in the form of hyperboloid of revolution surfaces on buckling resistance and stress-strain state is given in this paper, using the finite elements method in a computer software. Comparison is done with the result of the finite elements linear analysis of their buckling resistance.

PurposeThis paper aims to present development of a layer‐wise (LW) beam model for geometric nonlinear finite element analysis of laminated beams with partial layer interaction.Design/methodology/approachThe model is built assuming first order shear deformation theory (FSDT) at layer level and moderate interlayer slips. LW kinematic, strain and stress fields are established in view of co‐rotational finite element formulation. Laminated beam equilibrium relations are developed in strong, weak and matrix form. A notion of interface shear stress is used to define layer interactions.FindingsThrough suitable choice of kinematic model the co‐rotational approach is shown to provide means of obtaining robust finite element formulation for geometric nonlinear analysis of laminated structures with interlayer slips.Research limitations/implicationsThe proposed model is dedicated to geometric nonlinear finite element analysis of laminated beams undergoing large planar displacements, subject to small strains and moderate interlayer slips.Originality/valueNovelty of the proposed approach is based on encompassing shear deformations in geometric nonlinear analysis of laminated beams with interlayer slips. Arbitrary number of layers is considered.

A comparative study of shape imperfection and internal pressure effects on plastic, shakedown and elastic limit loads using large and small strain formulation of 90° pipe bends

Nonlinear large deformation analysis of shells using the variational differential quadrature method based on the six-parameter shell theory

Instead of using the previous straight beam element to approximate the curved beam, in this paper, a curvilinear coordinate is employed to describe the deformations, and a new curved beam element is proposed to model the curved beam. Based on exact nonlinear strain-displacement relation, virtual work principle is used to derive dynamic equations for a rotating curved beam, with the effects of axial extensibility, shear deformation and rotary inertia taken into account. The constant matrices are solved numerically utilizing the Gauss quadrature integration method. Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system. The present results are compared with those obtained by commercial programs to validate the present finite method. In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation, comparison of the results of the present formulation with those of the ADAMS software are made. Furthermore, the present results obtained from linear formulation are compared with those from nonlinear formulation, and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

Geometric nonlinear static analysis of structural systems with cable elements is carried out using point based iterative procedure. In all sub systems as cable systems, constituted for each node having at least one degree of freedom that is idealized by finite elements, successive calculations are performed. In the analysis part, based on finite element displacement method, to the maximum number of unknown displacements required for each sub-system calculation is limited with three. Tangent stiffness matrix, including pre-stressed internal forces as well as varying geometries with respect to different external force applications, is utilized. The convergence procedure is adapted into the method to prevent excessive displacements through the calculations. In the present study, a computer program has been developed to present a very effective calculation method. Different numerical applications have been considered and the results were compared with the literature results. Key words: Cable systems, nonlinear analysis, point based iterative procedure, convergence procedure.

Influence of boundary conditions and geometric imperfections on lateral–torsional buckling resistance of a pultruded FRP I-beam by FEA

The synchronous construction method of tower and beam can greatly shorten the construction period of cable-stayed bridge, but the force condition is complicated. The overall stability of the bridge which use synchronous construction method should be studied further. Based on the Dingzihekou Bridge project, a finite element analysis model was established and three typical construction conditions were selected by using Midas Civil software. Linear stability analysis and geometric non-linear stability analysis about the construction period of the Dingzihekou Bridge were conducted. The stability factors of the two construction schemes and the modes of the linear instability failure in the construction periods of the cable-stayed bridgeare inferred. It is found that the geometrically non-linear stability safety factor is significantly less than the linear. There is no big difference in linear stability factor between synchronous construction and asynchronous construction of tower and beam. As for the geometric nonlinear stability analysis, the synchronous construction of tower and beam has a larger stable safety factor than asynchronous construction.

The interlaminar fracture behavior of unidirectionally glass fiber reinforced composites with fiber surface treatments have been investigated in Mode I, Mode II and for a fixed mixed Mode 1/11 ratio. With respect to the loading conditions at the crack tip the double cantilever beam (DCB), the end notched flexure (ENF) and the mixed mode flexure (MMF) specimens were used in order to obtain Mode I, Mode II and mixed Mode I/II critical energy release rates. The data obtained from these tests have been analyzed by using analytical and finite element approaches. The present investigation is focused on the influence of the glass fiber surface treatment on the interlaminar fracture toughness. Glass fibers with two different fiber surface treatments have been investigated. For the DCB test the data reduction from the experiments have been carried out by using six different approaches: the area method. the Berry method, the modified beam analysis, the compliance method and the geometric linear and non-linear finite element analysis. The geometric non-linear finite element analysis of the DCB test was performed firstly. For the ENF test contact and friction along the crack surfaces have been taken into account.

The paper provides an overarching framework for the study of some of the intrinsic geometries that a topological group may carry. An initial analysis is based on geometric nonlinear functional analysis, that is, the study of Banach spaces as metric spaces up to various notions of isomorphism, such as bi-Lipschitz equivalence, uniform homeomorphism, and coarse equivalence. This motivates the introduction of the various geometric categories applicable to all topological groups, namely, their uniform and coarse structure, along with those applicable to a more select class, that is, (local) Lipschitz and quasimetric structure. Our study touches on Lie theory, geometric group theory, and geometric nonlinear functional analysis and makes evident that these can all be seen as instances of a single coherent theory.

Geometrical nonlinear and stability analysis for slender frame structures of crawler cranes

A reliable numerical procedure is proposed for the geometric nonlinear dynamic analysis of suspension bridges subjected to earthquake excitations. The geometric nonlinearities of cable members are captured by the catenary element derived from exact analytical expressions of elastic catenary, while the geometric nonlinearities of tower and girder members are predicted by nonlinear beam element which can undergo large deflections and rotations. An incremental-iterative solution based on Newmark-β direct integration and Newton–Raphson iteration is adopted for solving the nonlinear equation of motion. The results are compared with those generated by ANSYS to show the accuracy and efficiency of the proposed procedure.

The structural optimization of trusses is a complex problem that can be affected by many different factors. In this research, the authors investigated the optimization of trusses performing a geometric nonlinear analysis under dynamic loading, using two different metaheuristic algorithms: the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The objective function was to minimize the weight of the structure. A number of benchmark test problems for spatial trusses considering a geometric nonlinear analysis, and dynamic loading are analyzed to verify the performance of the optimization algorithms. The results showed that both algorithms were able to find efficient solutions to the optimization problem and suggest that the choice of the optimization algorithm can have a significant impact on the performance of the optimization process.

SummaryA recent unsymmetric 4‐node, 8‐DOF plane element US‐ATFQ4, which exhibits excellent precision and distortion‐resistance for linear elastic problems, is extended to geometric nonlinear analysis. Since the original linear element US‐ATFQ4 contains the analytical solutions for plane pure bending, how to modify such formulae into incremental forms for nonlinear applications and design an appropriate updated algorithm become the key of the whole job. First, the analytical trial functions should be updated at each iterative step in the framework of updated Lagrangian formulation that takes the configuration at the beginning of an incremental step as the reference configuration during that step. Second, an appropriate stress update algorithm in which the Cauchy stresses are updated by the Hughes‐Winget method is adopted to estimate current stress fields. Numerical examples show that the new nonlinear element US‐ATFQ4 also possesses amazing performance for geometric nonlinear analysis, no matter whether regular or distorted meshes are used. It again demonstrates the advantages of the unsymmetric finite element method with analytical trial functions.

Simplified nonlinear progressive collapse analysis of welded steel moment frames