Structure/load-dependent vectors for linear structural dynamic analysis

A structure/load-dependent vectors method is developed for large-scale, linear structural dynamic analysis with complex loadings. The dynamic solution vectors are used as starting vectors so that both structure and load characteristics are included in the basis vectors. This method requires less vectors for the same accuracy, especially for structures that have external concentrated masses. Numerical results are obtained to demonstrate the advantages of the present method over other reduction methods.

FEPACS (Finite Element Package for linear static, dynamic and instability Analysis of Composite Structures under hygro-thermo-mechanical loads) incorporates a complete library of consistent and correct 1-, 2- and 3-dimensional linear and quadratic general purpose finite elements. In this paper, we shall discuss the finite element technology that has gone into the package as well as its present modelling and solution capabilities. We shall also discuss briefly recent developments toward enhancing the package: Robust composite elements based on aC 0-continuous higher order transverse deformation plate/beam theory, and nonlinear element technology and solution strategies. Finally, we shall also briefly touch upon several satellite application modules that are in different stages of planning/development to aid FEPACS: damage assessment/prediction,expert-like advisors for solid modelling and finite element modelling/analysis, pre-/post-processing for FEPACS applications, structural optimisation and related finite element algorithms, and finally, a frontal solution module for FEPACS to enhance its feasibility for vectorisation/parallelisation.

This paper discusses implementation and adaptivity of the Discontinuous Galerkin (DG) finite element method as applied to linear and non-linear structural dynamic problems. By the DG method, both displacements and velocities are approximated as piecewise bilinear functions in space and time and may be discontinuous at the discrete time levels. Both implicit and explicit iterative algorithms for solving the resulted system of coupled equations are derived. They are third-order accurate and, while the implicit procedure is unconditionally stable, the explicit one is conditionally stable. An h-adaptive procedure based on the Zienkiewicz–Zhu error estimate using the SPR technique is applied. Numerical examples are presented to show the suitability of the DG method for both linear and non-linear structural dynamic analysis. Copyright © 1999 John Wiley & Sons, Ltd.

A review on computational linear and nonlinear dynamic analysis of shell-type composite structures

A simple and efficient modular simulation system is presented that enables conventional linear structural analysis programs to be used to model the collapse behavior of braced frames. With this tool and the availability of a linear structural model, accurate collapse analyses of complex structures can be performed in a few days. A foundation screening capability, based on the simulation concept, is also discussed - this is suitable for assessing rapidly the ultimate overturning resistance of piled foundations and can provide valuable information prior to performing a full system collapse analysis. These techniques, which are presently used within Shell in an operational environment, will enable practicing engineers to perform routinely in-house redundancy/overload checks on new structures, or collapse integrity assessments of existing structures, using standard linear structural analysis procedures. INTRODUCTION The majority of fixed offshore steel structures are designed and re-assessed using linear structural analysis programs, with acceptance criteria based on providing an adequate margin of safety against first member (or component) failure. In certain circumstances, however, one may wish to evaluate the collapse resistance (ultimate strength) of the structure - for example, to check the robustness of a new platform design or to re-assess the fitness for purpose of an existing structure that no longer complies with present design code recommended practice. These collapse assessments are usually carried out using cumbersome and complex non-linear analysis programs which require substantial expertise to use. In addition, these programs are generally not suited to routine applications. In this paper, a simple and efficient modular simulation system is presented that enables conventional linear structural analysis programs (SESAM, STRUDL, MARCS, SACS, etc.) to be used to model accurately the collapse behavior of frames in which the collapse mode is dominated by axial brace failure (buckling or yielding) or axial pile failure (pull-out or punch-through). Analysis experience has shown that for many braced steel frames, only these non-linearity's are important. The simulation technique is a modified form of the 'virtual distortion method' developed by Holnicki-Szulc & Gierlinski [1]. It is based on linear superposition and provides a phenomenological non-linear capability (i.e. the non-linear member data are prescribed by the user). Essentially the non-linear problem is reduced to finding a set of member end forces, Which, when combined with the applied loading, constrain the linear system to follow the behavior of the non-linear system. The set of constraining forces is usually quite small since, even for large structures, very few members (typically around ten) contribute to the collapse mechanism. This approach has several advantages over more complex non-linear analysis programs. Its major strength is that with the availability of a linear structural model and a suitable linear analysis program, a full collapse analysis of a complex structure can be performed within a few days. This contrasts with the several months required to regenerate the model and perform the analysis using a more complex non-linear analysis capability.

A growing attention has been addressed to the influence of infills on the seismic behavior of Reinforced Concrete buildings, also supported by numerical and experimental analyses, and by the observation of damage to infilled RC buildings after recent earthquakes (e.g. L'Aquila 2009, Lorca 2011, Emilia 2012). In this paper, the attention is focused on the Damage Limitation Limit State (DL LS), defined as dependent on displacement capacity limit directly related to the damage to infill panels. Although inelastic (post-cracking) displace- ment demand in RC members at this LS can be quite low, infill behavior can be already strongly non linear, if a diffuse state of cracking has begun to arise in infill panels. Thus, based on the results of several non linear dynamic analyses, a reduction factor of the initial elastic stiffness of infills is estimated, in order to obtain an effective stiffness of infill panels to be used in a linear analysis in order to obtain a displacement demand at DL LS (i.e., maxi- mum Interstorey Drift Ratio) which is approximately equal to the demand evaluated through non linear dynamic analysis on the same model. To this end, Incremental Dynamic Analyses (IDAs) are performed on four- and eight-storey infilled frames, designed for seismic loads according to the current Italian technical code and for gravity loads only according to an ob- solete technical code. Influence of number of storeys and design typology on the obtained ef- fective stiffness is also analyzed.

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

The structural analysis involves the definition of the model and selection of the analysis type. The model should represent the stiffness, the mass, and the loads of the structure. The structures can be represented using simplified models, such as the lumped mass models, and advanced models resorting the finite element method (FEM) and discrete element method (DEM). Depending on the characteristics of the structure, different types of analysis can be used such as limit analysis, linear and nonlinear static analysis, and linear and nonlinear dynamic analysis. Unreinforced masonry structures present low tensile strength, and the linear analyses seem to not be adequate for assessing their structural behavior. On the other hand, the static and dynamic nonlinear analyses are complex, since they involve large time computational requirements and advanced knowledge of the practitioner. The nonlinear analysis requires advanced knowledge on the material properties, analysis tools, and interpretation of results. The limit analysis with macro-blocks can be assumed as a more practical method in the estimation of maximum load capacity of structure. Furthermore, the limit analysis requires a reduced number of parameters, which is an advantage for the assessment of ancient and historical masonry structures, due to the difficulty in obtaining reliable data. The observation of the damage in masonry buildings caused by earthquakes in the past has been shown that the masonry structures can be discretized into several macro-blocks and interfaces. The macro-blocks are portions of a structure with similar material properties and structural behavior, to which the mechanical properties of the material can be assigned or, by simplification, they can be assumed to be infinitely rigid. The interfaces in a macro-modelling represent, in general, the cracks associated to the failure mechanisms. However, in a micro-modelling strategy applied to masonry, in which the units and the joints are individually considered, the interfaces simulate the behavior of the joints. Furthermore, different criteria for the strength parameters of macro-blocks and interfaces can be considered. The limit analysis (Fig. 1) with macro-blocks is a simplified and powerful structural analysis tool to evaluate the ultimate capacity of masonry structures by static models, involving the equilibrium of the macro-blocks through the limit analysis basic concepts.

In order to study the mechanical characteristics of the linear switched reluctance motors (LSRMs), modal analysis and linear static structure analysis of a LSRM is investigated in this paper. Basic theories of modal analysis and linear static structure analysis are stated. The structure of the LSRM is illustrated. And the modal analysis and linear static structure analysis by finite element method are demonstrated based on ANSYS workbench. The first six natural frequencies with the corresponding mode shapes and the deformation of the LSRM are obtained. The results show that the first six natural frequencies of the LSRM range from 2244.7 Hz to 4033.1 Hz, the deformation of the LSRM is within 0.0020546 mm under the largest normal force, and the easiest deformation part of the LSRM is the mover platform. The results verify that the mechanical design of the LSRM is reasonable.

The paper presents an equivalent linear modal analysis approach for calculating the seismic response of multi-degree-of-freedom structures with hysteretic stiffness elements. The hysteretic behavior is defined by the Bouc-Wen continuous model. The approach can be used with seismic inputs defined in terms of the pseudo acceleration and relative velocity ground response spectra which are commonly used in the analysis of linear structures. In addition to these conventionally used spectra, the need for defining the seismic input in terms of the velocity spectrum of a massless oscillator is also identified. The numerical results for the displacement response, and story shears obtained by this approach for a multi-story shear building are presented.

A new family of B-spline based explicit time integration methods for linear structural dynamic analysis

Uncertainty plays a fundamental role in structural engineering since it may affect both external excitations and structural parameters. In this study, the analysis of linear structures with slight variations of the structural parameters subjected to stochastic excitation is addressed. It is realistically assumed that sufficient data are available to model the external excitation as a Gaussian random process, while only fragmentary or incomplete information about the structural parameters are known. Under this assumption, a nonprobabilistic approach is pursued and the fluctuating properties are modeled as uncertain-but-bounded parameters via interval analysis. A method for evaluating the lower and upper bounds of the second-order statistics of the response is presented. The proposed procedure basically consists in combining random vibration theory with first-order interval Taylor series expansion of the mean-value and covariance vectors of the response. After some algebra, the sets of first-order ordinary differential equations ruling the nominal and first-order sensitivity vectors of response statistics are derived. Once such equations are solved, the bounds of the mean-value and covariance vectors of the response can be evaluated by handy formulas. To validate the procedure, numerical results concerning two different structures with uncertain-but-bounded stiffness properties under seismic excitation are presented.

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 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.

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.