Substructuring in linear and nonlinear analysis

The general purpose Finite Element system PERMAS has been ported to high parallel computer architectures in the scope of the ESPRIT project EUROPORT-1. We reported on the technical and theoretical background during the last HPCN conference. The parallelization rates and scalability achieved with this strategy are shown using both industrial relevant and artificial scalable examples. The behavior of the parallel version is studied on a parallel machine with a high speed communication network. The impact of the parallel version is not only a cost effective and fast solution for medium size Finite Element simulations, but also that extremely large industrial examples may be solved that until now were restricted to large supercomputers at very high cost. The results are discussed in view of the underlying approach and data structure.

Nonlinear structural analysis, which can account for geometrical or material nonlinearities beyond the scope of linear methods, typically incurs high computational costs. Recent advances have shown that quantum computers can accelerate various numerical simulations. Although quantum acceleration of linear structural analysis via the Quantum Linear System Algorithm (QLSA) has been studied, its application to nonlinear structural analysis remains unexplored. Here, we introduce our proposed quantum algorithm for accelerating nonlinear structural analysis, summarizing its key features and performance results from our recent study.

The article presents a finite element based study of linear and geometrically non-linear progressive failure analysis of thin walled composite aerospace structures subjected to combined in-plane and out-of-plane loading which are typically encountered in thin walled aerospace structures. Different ply and constituent based failure criteria and material property degradation schemes have been coded into a PCL code in Nastran. As case studies, progressive failure analyses of sample composite laminates with cut-outs under combined loading are executed to study the effect of geometric non-linearity on the first ply failure and progression of failure. Different ply and constituent based failure criteria and different material property degradation schemes are also compared in terms of predicting the first ply failure and failure progression. For mode independent failure criteria, a method is proposed for the determination of separate degradation factors for fiber and matrix failures which are assumed to occur simultaneously. The results of the present study, show that under combined out-of-plane and in-plane loading, depending on the load case linear analysis can significantly underestimate or overestimate the failure progression compared to geometrically non-linear analysis even at low levels of out-of-plane loading.

Wind resistant size optimization of geometrically nonlinear lattice structures using a modified optimality criterion method

Static and dynamic structural analyses of a turbine bladed-disk for a liquid rocket turbopump are performed to investigate the safety level of strength and vibration at design point. During operation, turbopump is exposed to various external loads. Therefore, the effects of them should be carefully considered and properly modeled. First, due to the high rotational speed of the turbopump, effects of centrifugal forces are considered in the structural analysis. Thermal load caused by severe temperature differences is also considered. A three dimensional finite element method (FEM) is used for linear and nonlinear structural analyses with modified Newton-Raphson iteration method. After the nonlinear solution is obtained from the structural analysis, dynamic characteristics are obtained as a function of rotational speed from the linearized eigenvalue analysis at an equilibrium position. From the analysis results, characteristics of stress distribution and vibration were thoroughly examined and investigated.

The success that has been achieved in applying optimization techniques to linear structural analyses has led to the desire to extend these techniques to nonlinear structural analyses. Studies have been done to apply both gradient and non-gradient based approaches to the nonlinear structural analysis problem. This paper presents a hybrid approach that enables the application of gradient based methods without incurring the expensive and difficult calculations required to provide sensitivities based on the nonlinear analysis. Specifically, it discusses the commercial implementation of the ESL (Equivalent Static Loads) method developed by Prof. G. J. Park and his research team into the MD Nastran computer code available from MSC Software. A high-level overview of the methods currently available to perform nonlinear structural optimization is followed by a brief review of the ESL method. Particular emphasis is placed on the special details required to place the prototype concepts into a commercial product. The implementation has emphasized placing minimal burden on the user to extend a file used as input to a nonlinear structural analysis task to one that can perform nonlinear structural optimization. Two examples are then provided to further illustrate the methods and demonstrate that it is capable of solving “real world” problems. Concluding remarks summarize the contributions of the paper and indicate further work that is being done at MSC to extend this initial implementation of nonlinear structural optimization.

The article presents a modified finite element (FE) based algorithm for non linear analysis of 2D beam structures, which takes into account the influence of the shear forces.The method proposed enables using complex materials with nonlinearities without the need of implementing advanced constitutive models in FE routines.It can be directly inte grated with commonly available FE software for linear analysis of beam structures, so its functionality can be easily extended also with material nonlinearities.The presented approach adopts the generalized constitutive law algorithm to iteratively modify the stiffness of beam element.To address an influence of a shear stiffness, a Timoshenko beam element was used.The methodology was implemented and its performance was verified on several numerical examples.For validation, the displacements and the ultimate loads were compared with the values from a commercial FE software.The results shown a good correlation between the ref erence model and the method proposed.

This paper gives a general overview of the analysis of offshore structures under fire loads. Attention is drawn to the different requirements of component fire testing, which may give misleading emphasis to certain types of analysis. It is shown that the basis of structural behaviour under fire loading is the change in material properties. However, it is the effects of thermal strains which are most likely to promote structural instability, leading to collapse. Non-linear structural analysis has ban USCXI to illustrate fire loading effects, but it is likely that the offshore design industry will employ linear elastic structural analysis in many designs. The design of seeondary structures to reskt fire loadings is discussed. INTRODUCTION The design of steel offshore structures to resist fire loadings is a new technology. Analytical techniques are not particularly well developed [1,2] or understood by either practicing engineers who develop the designs or safety specialists, who overview the design process. What is well understood is the technology of fire component testing [3,4], and it is this knowledge which is perhaps misleading the development of the analysis of steel structures under fire loadings. Recent research into structural fire performance has concentrated on the numerical simulation of furnace fire tests. Whereas such work [5] can lead to economies in component testing programs it does little to increase the fundamental understanding of full-scale structures in real fires. Offshore fires involve a hydrocarbon inventory, and embrace jet, pool and running liquid fire types. The description and calculation of fire loadings is not addressed in this paper. Material Behaviour The behaviour of steel structures under fire loading conditions is determined largely by temperature related material properties. Foundation data is available from a number of sources [6,7,8,9]. It is conventional to split the material properties into two groups. These are then termed the thermal and the mechanical material properties. Thermal properties are:specific heat,thermal conductivitycoefficient of thermal expansion.The mechanical properties are:yield stress (Fy),Youngs modulus (E),Shear modulus (G). Almost without exception, the material properties of steel vary to a greater or lesser extent with temperature. The stress-strain behaviour of a typical structural steel is shown in Figure 1. Note the loss of a sharp yield point and the drop in performance between 400 deg C and 750 deg C. When a steel type has been given enhanced properties by heat treatment, then the properties are likely to fall-back to those associated with the chemical composition when a threshold temperature of about 600 deg C is attained in a fire. By contrast the material properties associated with microstructure and hence chemical composition are both enduring and pertinent to fire conditions. In Figure 2 the behaviour of Austenitic stainless steel, low carbon structural steel and 'fire-resisting' steel are compared. In the range 600 deg C to 800 deg C the stainless steel retains more of its basic strength.

This comprehensive textbook combines classical and matrix-based methods of structural analysis and develops them concurrently. It is widely used by civil and structural engineering lecturers and students because of its clear and thorough style and content. The text is used for undergraduate and graduate courses and serves as reference in structural engineering practice. With its six translations, the book is used internationally, independent of codes of practice and regardless of the adopted system of units. Now in its seventh edition: the introductory background material has been reworked and enhanced throughout, and particularly in early chapters, explanatory notes, new examples and problems are inserted for more clarity., along with 160 examples and 430 problems with solutions. dynamic analysis of structures, and applications to vibration and earthquake problems, are presented in new sections and in two new chapters the companion website provides an enlarged set of 16 computer programs to assist in teaching and learning linear and nonlinear structural analysis. The source code, an executable file, input example(s) and a brief manual are provided for each program.

An efficient stochastic finite element method is proposed for the reliability analysis of nonlinear frame structures using the first-order second-moment reliability method. The assumed stress-field approach is used in computing nonlinear structural responses and the corresponding response gradients. Both geometric and material nonlinearities of structures are considered. The flexibility of a connection is represented by its moment-relative rotation relationship. Emphasis is placed on the comparison of the reliability indexes of linear structures, nonlinear structures, and nonlinear structures with flexible connections. Both the strength (combined axial compression and bending) and serviceability (deflection) limit states are considered. For stability-related structures, nonlinearity has a considerable influence on the structural reliability, and the reliability will be very different when the flexible connections are taken into consideration. The method is verified using the Monte Carlo simulation technique. The applicability, accuracy, efficiency, and robustness of the method are verified with the help of an example.

In this work, we describe the formulation and implementation for stress-based hybrid elements for conducting non-linear analysis of elastic structures. The motivation behind developing these elements is that they should be as simple to use as standard displacement-based isoparametric brick elements, but at the same time, be relatively immune to the shortcoming that these elements suffer from, namely, ‘locking’ problems which occur when they are used to model plate/shell geometries, almost incompressible materials or when the elements are distorted, and so on. The formulation is based on a two-field mixed variational principle. Numerical examples are presented to demonstrate the excellent performance of the proposed elements on a variety of challenging problems involving very large deformations, buckling, mesh distortions, almost incompressible materials, etc. Copyright © 2006 John Wiley & Sons, Ltd.

A seismic free field input formulation of the coupling procedure of the finite element (FE) and the scaled boundary finite-element (SBFE) is proposed to perform the unbounded soil-structure interaction analysis in time domain. Based on the substructure technique, seismic excitation of the soil-structure system is represented by the free-field motion of an elastic half-space. To reduce the computational effort, the acceleration unit-impulse response function of the unbounded soil is decomposed into two functions; linear and residual. The latter converges to zero and can be truncated as required. With the prescribed tolerance parameter, the balance between accuracy and efficiency of the procedure can be controlled. The validity of the model is verified by the scattering analysis of a hemi-spherical canyon subjected to plane harmonic P, SV and SH wave incidence. Numerical results show that the new procedure is very efficient for seismic problems within a normal range of frequency. The coupling procedure presented herein can be applied to linear and nonlinear earthquake response analysis of practical structures which are built on unbounded soil.

A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic distribution parameters is proposed. The partial differential equation with spatial varying parameters for nonlinear vibration of beams with periodic parameters under harmonic excitations is derived. The procedure of the multimode perturbation method includes three main steps: first, the nonlinear partial differential equation is transformed into linear partial differential equations with varying parameters by applying perturbation method; second, the linear partial differential equations are transformed into ordinary differential equations with multimode coupling by applying Galerkin method, where multiple vibration modes of the beams are used and the equations are suitable to nonlinear vibration of periodic structures with high parameter-varying wave in wide frequency band; third, the ordinary differential equations are solved by applying harmonic balance method to obtain vibration response of the nonlinear periodic beam, which is used for characteristics analysis of frequency response and spatial mode. Furthermore, the stability problem of nonlinear harmonic vibration as multidegree-of-freedom system with periodic time-varying parameters is solved by applying direct eigenvalue analysis approach. The proposed method can incorporate multiple vibration modes into response analysis of nonlinear periodic structures and consider mode-coupling effects due to structural nonlinearity and parametric periodicity. Finally, a nonlinear beam with periodic supports under harmonic excitations is studied. Numerical results on frequency response of the beam are given to illustrate an application of the proposed method, new frequency response characteristics, and influences of periodic parameters on structural response. The results have potential application to nonlinear structural vibration control and support damage detection of nonlinear structures with periodic supports.

Comparison of ACI-318 and TS-500 codes for nonlinear seismic analysis of RC structures using force-based fiber element approach

Pre-tensioned cable net systems are being increasingly used in building façades. Due to the geometrical nonlinearities exhibited by the cables, people have to resort to the nonlinear response history analysis approach for analyzing the seismic responses of cable net structures. This article studies the effectiveness of linear response spectrum analysis method for nonlinear cable net systems. An energy-based parameter is used to describe the structural stiffness, based on which the equivalent single-degree-of-freedom systems for cable net structures with various irregularities could be established. By means of a pseudo-energy-equivalent approach, the nonlinear equivalent single-degree-of-freedom systems are transformed into linear ones, whose seismic responses are reasonable approximations of the accurate nonlinear results. It is revealed that the vibrating period of the equivalent linearized system is close to that of the nonlinear equivalent single-degree-of-freedom system, indicating that the nonlinear effects on seismic responses of cable net structures are not serious. Inspired by the theoretical analysis, large-scale numerical computations are carried out to check the accuracy of linear response spectrum analysis for nonlinear cable net structures. In the numerical computation, four cable net models are excited by 80 seismic records. Considering 19 different degrees of earthquake intensity, a total number of 6080 nonlinear response history analyses are executed, and the results are compared with those obtained from the linear response spectrum analysis. From the numerical results, the linear response spectrum analysis yields proper overestimations of seismic responses with errors within 35%, which may lead to slightly conservative yet acceptable designs in engineering practice. Given all the aforementioned discussions, it is concluded that the linear response spectrum analysis method is effective for seismic response analysis and aseismic design of nonlinear cable net structures.