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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 design of compliant towers in deep waters is greatly affected by their dynamic response to wave loads as well as by the geometrical and material nonlinearities that appear. In general, a nonlinear time history dynamic analysis is the most appropriate one to be applied to capture the exact response of the structure under wave loading. However, this type of analysis is complex and time-consuming. This paper aims to develop a simplified methodology, which can adequately approximate the maximum response yielded by a dynamic analysis by means of a static analysis.

Various types of time history dynamic analysis are first applied on a detailed structural model, ranging from linear to fully nonlinear, that are used as reference solutions. In the sequel, a simplified analysis model is formulated, capable of reproducing the response of the entire structure with significantly reduced computational cost. In the next stage, this model is used to obtain the linear and nonlinear response spectra of the structure. Finally, these spectra are used to formulate a simplified design approach, based on equivalent static loads.

This simplified design approach produces good results in cases that the response is mainly governed by the first eigenmode, which is the case when compliant towers are considered.

The present paper borrows ideas from the area of earthquake engineering, where simplified methodologies can be used for the design of a certain class of structures. However, the development of a simplified methodology for the approximation of the dynamic behavior of offshore structures under wave loading is a much more complex problem, which, to the authors’ knowledge, has not been addressed till now.

This study examines two distinct bearing stiffness calculation methods, both of which are based on the displacement-load function. Previous research typically incorporated one type of bearing stiffness into their system mechanics or vibration analysis. However, these two methods of calculating stiffness lead to different vibration models. This implies that the choice for vibration investigation is not merely about selecting one of the two types of stiffness, but also about how to appropriately implement that chosen stiffness within a model. The primary objective of this work is to compare these two methods of bearing calculation and to discuss the suitable applications of each method in both static and dynamic analyses.

This study compares two distinct methods for calculating bearing stiffness. It explores the relationships between varying bearing stiffnesses, their internal structures, and contact features. Furthermore, it examines the impact of external loads on the static properties and dynamic characteristics of different bearing stiffnesses. Finally, based on the outcomes observed under various operating conditions, the study discusses the suitability of each method for static and dynamic analysis.

Mean stiffness is more suitable for calculating load transmissibility in a static state or capturing the delivery performance at instantaneous equilibrium positions in a dynamic state. Since the variation of the equilibrium positions is ignored, the alternating stiffness model is better suited for capturing the fluctuating properties of the vibration behaviors, especially under variable external load conditions.

We compare the two bearing calculation methods and discuss the appropriate applications of each method for static and dynamic analysis.

Progressive collapse refers to a phenomenon, in which local damage in a primary structural component leads to total or partial structural system failure, without any proportionality between the initial and final damage. Robustness is a measure that demonstrates the strength of a structure to resist progressive collapse. Static pushdown and nonlinear dynamic analysis were two main procedures to calculate the capacity of structures to resist progressive collapse. According to previous works, static analysis would lead to inaccurate results. Meanwhile, capacity analysis by dynamic analysis needs several reruns and encountering numerical instability is inevitable. The purpose of this paper is to present the formulation of a solution procedure to determine robustness of steel moment resisting frames, using plastic limit analysis (PLA).

This formulation utilizes simplex optimization to solve the problem. Static pushdown and incremental dynamic methods are used for verification.

The results obtained from PLA have good agreement with incremental analysis results. While incremental dynamic analysis is a very demanding method, PLA can be utilized as an alternative method.

The formulation of progressive collapse resistance of steel moment frames by means of PLA is not proposed in previous research works.

This paper presents several methods for enhancing computational efficiency in both static and dynamic analysis of structural systems with localized non‐linear behaviour. A significant reduction of computational effort with respect to brute‐force non‐linear analysis is achieved in all cases at the insignificant (or no) loss of accuracy. The presented methodologies are easily incorporated into a standard computer program for linear analysis.

A method for non‐linear static and dynamic analysis of flexible systems submerged in water is outlined. The systems considered here include cable and beam elements, as well as buoys and clump weights. Contact and lift‐off between members and the sea floor is also accounted for. The formulation used allows for very large deformations and material non‐linearities. Hydrostatic buoyancy and hydrodynamic drag forces are considered throughout the analyses. These capabilities have been implemented in the general purpose non‐linear finite element program FENRIS. Aspects concerning efficient solution of the non‐linear static and dynamic equations are discussed. In particular, an efficient start‐up procedure for analysis of highly flexible systems is described. The paper shows applications involving static and dynamic analysis of a floating structure kept in place by six mooring lines and a flexible riser system.

This paper 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 bibliography at the end of the paper contains more than 1330 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 1999–2002.

A thermal analogy method for the static and dynamic analysis of an electrostrictive beam by incorporating the nonlinear characteristics of the electrostrictive materials is described in this paper. The analogy between thermo elastic finite element formulation and the electrostrictive material finite element formulation developed in this paper was explored. Based on this analogy, the voltage actuation of the electrostrictive beam can be simulated accurately using the conventional elastic finite element model with the thermal actuation. The finite element model includes the quadratic dependence of strain with electric field, valid at constant temperature and mechanical prestress, and excludes hysteresis.

As compared with homogeneous metals and alloys, cellular metals provide low density, high specific stiffness, high energy absorption and good damping, thus being interesting alternatives to employ as protection against shock and impact. Impact energy is dissipated through cell bending, buckling or fracture. The knowledge and computational modelling of the mechanical behaviour of metal foams structures is thus of great importance for real life applications. The purpose of this paper is to increase the knowledge of the differences in metallic hollow sphere structures' (MHSS) behaviour under dynamic loading, as compared with the corresponding behaviour under static loading and to determine the influence of inertia and loading rate.

Computational dynamical finite element analyses of representative volume elements (RVE) of MHSS have been performed considering varying loading rates. Partially bonded geometries are considered and the effect of the spheres' distribution is also taken into account.

The results of the numerical examples presented show that inertia plays an important role in the dynamic behaviour of this kind of energy‐absorbing structure. When compared with the corresponding values in the quasi‐static case, the effect of inertia makes the peak load higher. If the deformation rate is higher (greater than 1.39 m/s in the studied cases), the characteristic plateau usually present in compressed metal foams can vanish. For the geometries analysed, damage has a small influence on load‐deformation relations.

This paper presents and discusses differences between static and dynamic behaviour of partially bonded MHSS. There are few references in the literature covering this issue by means of numerical analysis.

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 is given. The bibliography at the end of the paper contains 1,726 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 1996‐1999.