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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.

While calculating internal forces of a structure resulting from temperature it is necessary to know thermal conduction and what goes hand in hand to determine temperature distribution at various points of the analysed structures. Finite strip method (FSM) is very suitable for the analysis of thermal conduction, heating, heat and temperature distribution in engineering structures, especially rectangular of identical edge conditions. The paper presents several examples of FSM application for the analysis of conduction and heat and temperature distribution for various types of engineering structures which can appear, among others, while welding several joined elements with welds made at specified speed as linear and point welds. Bars, shields, square and rectangular plates, steel orthotropic plates, steel and combined girders (steel‐concrete), box girders subject to various loads connected with heat and temperature (loaded with temperature, non‐uniformly heated surface). The obtained results may be useful in engineering practice for determining actual temperature and load capacity in individual elements of the construction.

The finite strip method has been shown to apply to many problems in continuum mechanics. Within the constraints of the method, it has been shown to be superior to the finite element method in terms of data preparation, program complexity and execution time. The finite strip method has been recently extended to groundwater flow problems. The orthogonality of appropriately selected shape functions gives the finite strip method its computational efficiency. The uncoupling achieved from this orthogonality also produces a numerical method which is intrinsically parallel. Consequently, additional efficiencies can be obtained in a parallel environment. Numerical studies of the finite strip method to model a two‐dimensional groundwater flow problem demonstrate the accuracy of the solution and the superior performance of the numerical procedure in a parallel environment.

A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin shell theory is presented. Details of obtaining all relevant strip matrices and vectors are given. It is also shown how the use of the simple linear two node strip with reduced integration leads to direct explicit forms of all relevant matrices. Examples of application which show the accuracy of the linear strip for free vibration analysis of structures are presented.

This paper deals with structural shape optimization of vibrating prismatic shells and folded plates. The finite strip method is used to determine the natural frequencies and modal shapes based on Mindlin‐Reissner shell theory which allows for transverse shear deformation and rotatory inertia effects. An automated optimization procedure is adopted which integrates finite strip analysis, parametric cubic spline geometry definition, automatic mesh generation, sensitivity analysis and mathematical programming methods. The objective is to maximize the fundamental frequency by changing thickness and shape design variables defining the cross‐section of the structure, with a constraint that the total volume of the structure remains constant. A series of examples is presented to highlight various features of the optimization procedure as well as the accuracy and efficiency of finite strip method.

This paper aims to analyze the stability of laminated shells subjected to axial loads or external pressure with considering various geometries and boundary conditions. The main aim of the present study is developing an efficient combined method which uses the advantages of different methods, such as finite element method (FEM) and isogeometric analysis (IGA), to achieve multipurpose targets. Two types of material including laminated composite and sandwich functionally graded material are considered.

A novel type of finite strip method called isogeometric B3-spline finite strip method (IG-SFSM) is used to solve the eigenvalue buckling problem. IG-SFSM uses B3-spline basis functions to interpolate the buckling displacements and mapping operations in the longitudinal direction of the strips, whereas the Lagrangian functions are used in transverse direction. The current presented IG-SFSM is formulated based on the degenerated shell method.

The buckling behavior of laminated shells is discussed by solving several examples corresponding to shells with various geometries, boundary conditions and material properties. The effects of mechanical and geometrical properties on critical loads of shells are investigated using the related results obtained by IG-SFSM.

This paper shows that the proposed IG-SFSM leads to the critical loads with an approved accuracy comparing with the same examples extracted from the literature. Moreover, it leads to a high level of convergence rate and low cost of solving the stability problems in comparison to the FEM.

The purpose of this paper is to develop and apply an exact finite strip (F‐a FSM) for the buckling and initial post‐buckling analyses of box section struts.

The Von‐Karman's equilibrium equation is solved exactly to obtain the buckling loads and deflection modes for the struts. The investigation is then extended to an initial post‐buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. Through the solution of the Von‐Karman's compatibility equation, the in‐plane displacement functions are developed in terms of the unknown coefficient. These in‐plane and out‐of‐plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient.

The F‐a FSM is applied to analyze the buckling and initial post‐buckling behavior of some representative box sections for which the results were also obtained through the application of a semi‐energy finite strip method (S‐e FSM). For a given degree of accuracy in the results, however, the F‐a FSM analysis requires less computational effort.

In the present F‐a FSM, only one of the calculated deflection modes is used for the initial post‐buckling study.

A very useful and computationally economical methodology is developed for the initial design of struts which encounter post‐buckling.

The originality of the paper is the fact that by incorporating a rigorous buckling solution into the Von‐Karman's compatibility equation, and solving it, a fairly efficient method for post‐buckling stiffness calculation is achieved.

This paper deals with the buckling analysis of prismatic folded plate structures supported on diaphragms at two opposite edges. The analysis is carried out using variable thickness finite strips based on Mindlin‐Reissner assumptions which allow for transverse shear deformation effects. The theoretical formulation is presented for a family of C(0) strips and the accuracy and relative performance of the strips are examined. Results are presented for a series of problems including plates and stiffened panels. In a companion paper these accurate and inexpensive finite strips are used in the context of structural shape optimization.

An analysis of the plate and folded plate structures is carried out, taking into account the geometrical non‐linearities and the effects of creep, using the finite strip method. An assumption is made that only small deformations and large displacements and rotations exist. Creep of concrete has an important influence on some structures and cannot be neglected in such analysis, especially when geometrical non‐linearities are taken into account. The stiffness matrices (classical and geometrical) and the vector of equivalent nodal loading for the finite strips are obtained using the variation approach. The interpolation functions used are multiples of polynomial and trigonometric functions. Numerical examples showing the theoretical considerations are presented.

The problems of inelastic instability (buckling) and dynamic instability (resonance) have been the subject of extensive investigation and have received wide attention from the structural mechanics community. This paper aims to tackle these problems in thin-walled structures, taking into account geometrical and/or material non-linearity.

The inelastic buckling mode interactions and resonance instabilities of prismatic thin-walled columns are analysed by implementing the semi-analytical finite strip method (FSM). A scalar damage parameter is implemented in conjunction with a material modelling named rheological-dynamical analogy to address stiffness reduction induced by the fatigue damage.

Inelastic buckling stresses lag behind the elastic buckling stresses across all modes, which is a consequence of the viscoelastic behaviour of materials. Because of the lag, the same column length does not always correspond to the same mode at the elastic and inelastic critical stress.

This paper presents the influence of mode interactions on the effective stresses and resonance instabilities in thin-walled columns due to the fatigue damage. These mode interactions have a great influence on damage variables because of the fatigue and effective stresses around mode transitions. In its usual semi-analytical form, the FSM cannot be used to solve the mode interaction problem explained in this paper, because this technique ignores the important influence of interaction of the buckling modes when applied only for undamaged state of structure