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Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The first part of this paper presents an incremental variational principle and an incremental finite element in time‐space domain for the analysis of large amplitude, periodic vibration of multilayer sandwich plates. A reduced basis composed of eigenvectors corresponding to linear free vibration is introduced to reduce the order of the resulting linearized equations governing the non‐linear motion which are solved incrementally in association with Newton‐Raphson iterative method and an extrapolating technique. In the second part the solution techniques are described in detail and a number of examples on various non‐linear responses of rectangular multilayer sandwich plates, including superharmonic, subharmonic and internal resonance, are included in the study. Viscous modal damping is also considered when the structure is under forced excitation.

A simple numerical algorithm is developed for the implementation of the harmonic balance method to analyse periodic responses of a general dynamic system having geometrical non‐linearities of the quadratic and cubic types. The resulting non‐linear algebraic equations which are not explicitly determined are solved by non‐linear equation routines available in most mathematical libraries. Various non‐linear responses, such as the combinational resonances of a hinged‐clamped beam, the non‐linear effect on degenerate vibration modes of a square plate and the non‐linear oscillation of thin rings, are presented to demonstrate the versatility of the algorithm.

The purpose of this paper is to mainly review the state-of-the-art developments in the field of hydrodynamics of offshore pipelines, identifying the key tools for analysis of pipeline free spans, their applications, their qualifying characteristics and capabilities and limitations.

These different analytical, numerical and semi-empirical tools available for predicting such hydrodynamic loads and their effects include VIVANA, PIPESIN, VIVSIM, SIMULATOR, FATFREE, amongst others. Inherent in these models are current effects, wave effects and/ or pipe–soil interactions.

Amongst these models, the most attention was given to the new VIVANA model because this model take into account the vortex-induced effects with respect to free-spanning pipelines (which have dominant effect in the span analysis in deep water) better than other semi-empirical models (such as Shear 7). Recent improvements in VIVANA include its ability to have arbitrary variation in speed and direction of current, as well as the ability for calculation of pure IL and combined IL-CF response. Improvements in fatigue assessments at free spans, i.e. pipe–soil interaction have been achieved through the combined frequency domain and non-linear time domain analysis methodology adopted. Semi-empirical models are still the de facto currently used in the design of free-spanning pipelines. However, there is need for further research on free-span hydrodynamic coefficients and on how in-line and cross-flow vibrations interact. Again, there is still the challenge due to VIV complexity in fully understanding the fluid structure interaction problem, as there is no consolidated procedure for its analysis. It has been observed that there is large scatter between the different codes adopted in the prediction of fatigue damage, as there lacks full-scale test data devoted to determination/validation of the coefficients used in the semi-empirical models. A case study of the preliminary design of a typical 48 in. pipeline has been presented in this study to demonstrate the use of the free-span analysis tool, DNV RP F105. Excel spreadsheet has been applied in the execution of formulas.

This review paper is the first of its kind to study the state-of-the-art development in pipeline free-span analysis models and demonstrate the use of analysis tool, DNV for MAFSL calculation. Hence, information obtained from this paper would be invaluable in assisting designers both in the industry and academia.

The theoretical development of the incremental finite element for non‐linear vibration of multilayer sandwich plates was presented in Part 1 and the equation of motion was established. In the second part of the paper, the solution techniques are described and a number of examples are given.

Condition assessment on reinforced concrete (RC) structures is one of the critical issues as a result of structure degradation due to aging in many developed countries. The purpose of this paper is to examine the sensitivity and reliability of the conventional dynamic response approaches, which are currently applied in the RC structures. The key indicators include: natural frequency and damping ratio. To deal with the non-linear characteristics of RC, the concept of random decrement is applied to analyze time domain data and a non-linear damping curve could be constructed to reflect the condition of RC structure.

A full-scale RC structure was tested under ambient vibration and the impact from a rubber hammer. Time history data were collected to analyze dynamics parameters such as natural frequency and damping ratio.

The research demonstrated that the measured natural frequency is not a good indicator for integrity assessment. Similarly, it was revealed that the traditional theory of viscous damping performed poorly for the RC with non-linear characteristics. To address this problem, a non-linear curve is constructed using random decrement and it can be used to retrieve the condition of the RC structure in a scientific manner.

The time domain analysis using random decrement can be used to construct a non-linear damping curve. The results from this study revealed that the damage of structure can be reflected from the changes in the damping curves. The non-linear damping curve is a powerful tool for assessing the health condition of RC structures in terms of sensitivity and reliability.

This bibliography contains references to papers, conference proceedings, theses and books dealing with finite strip, finite prism and finite layer analysis of structures, materially and/or geometrically linear or non‐linear.

The purpose of this paper is to develop a general mathematical model for laminated curved structure of different geometries using higher-order shear deformation theory to evaluate in-plane and out of plane shear stress and strains correctly. Subsequently, the model has to be validated by comparing the responses with developed simulation model (ANSYS) as well as available published literature. It is also proposed to analyse thermal buckling load parameter of laminated structures using Green–Lagrange type non-linear strains for excess thermal distortion under uniform temperature loading.

Laminated structures known for their flexibility as compared to conventional material and the deformation behaviour are greatly affected due to combined thermal/aerodynamic environment. The vibration/buckling behaviour of shell structures are very different than that of the plate structures due to their curvature effect. To model the exact behaviour of laminated structures mathematically, a general mathematical model is developed for laminated shell geometries. The responses are evaluated numerically using a finite element model-based computer code developed in MATLAB environment. Subsequently, a simulation model has been developed in ANSYS using ANSYS parametric design language code to evaluate the responses.

Vibration and thermal buckling responses of laminated composite curved panels have been obtained based on proposed model through a customised computer code in MATLAB environment and ANSYS simulation model using ANSYS parametric design language code. The convergence behaviour are tested and compared with those available in published literature and ANSYS results. Finally, the investigation has been extended to examine the effect of different parameters (thickness ratios, curvature ratios, modular ratios, number of layers and support conditions) on the free vibration and thermal buckling responses of laminated curved structures.

The present paper intends to give sufficient amount of numerical experimentation, which may lead to help in designing of finished product made up of laminated composites. Most of the aerospace, space research and defence organisation intend to develop low cost and high durable products for real hazard conditions by taking combined loading and environmental conditions. Further, case studies might lead to a lighter design of the laminated composite panels used in high-performance systems, where the weight reduction is the major parameter, such as aerospace, space craft and missile structures.

In this analysis, the geometrical distortion due to temperature is being introduced through Green–Lagrange sense in the framework of higher-order shear deformation theory for different types of laminated shells (cylindrical/spherical/hyperboloid/elliptical). A simulation-based model is developed using ANSYS parametric design language in ANSYS environment for different geometries and loading condition and compared with the numerical model.

The purpose of this paper is to carry out free vibration and buckling analysis of functionally graded material (FGM) plate.

Equilibrium and stability equations of FGM rectangular plate under different boundary conditions are derived using finite element method-based inverse trigonometric shear deformation theory (ITSDT). Eight-noded rectangular plate element with seven degrees of freedom at each node is used for the present analysis. The power-law distribution method has been considered for the continuously graded variation in composition of the ceramic and metal phases across the thickness of a functionally graded plate.

The finite element formulation incorporated with ITSDT and provisions of the constitutive model of FGM plate has been implemented in a numerical code to obtain the natural frequency and critical buckling load under uniaxial and biaxial compressive load. The influence of material gradation, volume fraction index, span to thickness ratio and boundary constraints over free vibration and buckling response has been studied.

Development and validation of finite element methodology using ITSDT to predict the structural response of the FGM plates under different loading, geometric and boundary conditions.

The current trend in ground resonance testing is aimed at providing aircraft modes of vibration appropriate to the free‐free condition. To achieve this objective the rigid body frequencies of the aircraft on its supports must be low by comparison with the frequency of any mode of distortion. A minimum frequency ratio of 1:3 is specified. The various types of support in current use are considered in relation to the minimum frequency they are likely to provide. It appears that none are capable of frequencies lower than about 0·5 cycles/sec. For the forthcoming generation of large thin‐wing aircraft with fundamental frequencies below 1 cycle/sec. some further development in methods of support seems necessary. A non‐linear spring system appears to hold great promise in this respect, and one such system is described capable of frequencies less than 0·25 cycles/sec. for a limited range of movement.