Structural analysis of a prestressed concrete

The stiffness or displacement method for analyzing structures is exemplified by means of trusses. This type of structure has been relatively neglected until now because, in the view of the author, truss analysis by the force method is numerically too cumbersome. The stiffness method, on the other hand, is totally independent of the type of structure and applies with equal ease to trusses, beams and frames. We, of course, bear in mind that the computations are all computerized.

An analytical solution to the problem of the stress-strain state of a long cylindrical shell supported by two identical side elements of rectangular cross-section is proposed. As a rule, cylindrical shells have side elements in which the main tensioned reinforcement is placed, which significantly reduces the magnitude of tensile stresses, reduces vertical and horizontal displacements of the shell edges. The choice of the type of side elements depends mainly on the conditions of support of the shell edges. Proposals for accounting for the operation of side elements are presented only in regulatory documents and relevant manuals to them. The algorithm proposed by the authors involves the implementation of two approaches ― calculation according to the general semi-moment-free theory and calculation with simplifying hypotheses for shallow shells of medium length. In the first case, the problem is reduced to a system of four linear equations. From this system, it is possible to determine the forces and displacements due to the action of additional edge forces, as well as add them with individual components of the moment-free stress state, to obtain the total forces and displacements in the shell. Two separate cases are considered: gentle cylindrical shells of medium length (the method of forces and the method of displacements are used, the case when the side element is absolutely flexible in some direction is additionally considered) and multi-wave shells in which the side element is loaded by edge forces from both sides (the method of forces is used, symmetric and skew-symmetric loading are considered).

Of the two main finite element approaches, the displacement method has progressed more rapidly than the force method in the area of element representation. Many authors have contributed to the displacement method with both static and dynamic stiffness matrices for beam elements, plane stress elements and plate bending elements. The plane stress and bending elements being rectangular, triangular or quadrilateral in form. A dynamic stiffness matrix consists of a static stiffness matrix and a mass matrix. In the force method, .static flexibility matrices have been developed for beam elements and plane stress elements. However, static flexibility matrices for plate bending elements have only recently been published (Kaufman and Hall, Morley, Robinson, Przemieniecki). For the past few years, the author has been investigating the rank force method for structural vibration analysis. In ref. 6 a dynamic flexibility matrix is presented for a beam element. This matrix consists of a static flexibility matrix and an inverse mass matrix. Ref. 5 contains the derivation of a dynamic flexibility matrix for a rectangular plate element in bending, twisting and shear. The author, in collaboration with Petyt, demonstrated how a dynamic stiffness and flexibility matrix can be extended to include material damping.

This paper presents static and dynamic analysis of tower structure supporting a 600KW wind turbine based on the theory of FEM. According to the static and dynamic characteristics of tower structure, the works about simplified models and confirming loads and boundary condition are discussed. In static analysis, under different work conditions the load bearing capacity of tower structure is analyzed with door opening in different directions and without door opening. In dynamic analysis, in order to address the impacts of the foundation on structure, the research discusses the natural frequency and eigenmode from the first sixth modes at the assumption of fixed base and the elastic subgrade. Comparative studies have been performed on the results of the above analysis and some useful conclusions are drawn pertaining to the effectiveness and accuracy of the various models used in the work. Our research work lays a solid foundation of the further static and dynamic analysis.

A time-domain spectral element method with C1 continuity for static and dynamic analysis of frame structures

Relevance . Dynamic analysis of complex structures using numerical methods leads to the solution of the algebraic problem of eigenvalues and the corresponding eigenvectors of high orders. The solution of this problem for high order matrices is performed using reduction methods. One of the most effective methods is the method of sequential frequency-dynamic condensation, which allows partial consideration of the dynamic properties of the structure in the minor degrees of freedom. This allows for more accurate results compared to static condensation. Frequency-dynamic condensation is traditionally used to reduce frequency equations derived from the finite element method in the form of the displacement method or the force method. Methods. The authors have developed an algorithm for the frequency-dynamic condensation method for the frequency equation obtained on the basis of the FEM in the form of the classical mixed method. That allows to obtain not only the spectrum of the lower vibration frequencies, but also the corresponding vibration modes and the stress-strain state of the structure. Results . This article describes the algorithm and its practical implementation in the problem of dynamic analysis of a rectangular plate. The results of the numerical analysis of the problem are presented. An assessment of the accuracy of the method and recommendations for its use are given.

In this study, the graph-theoretic force method is applied to the optimal design of frame structures and systematically compared with the conventional displacement method. The optimization is performed using the Water Strider Algorithm (WSA), a recently developed bio-inspired metaheuristic, whose population-based search strategy is integrated with both analysis approaches. To ensure reproducibility, all key WSA parameters are reported, and large-scale highly indeterminate frame examples (up to 292 members) are tested, extending beyond previous benchmark studies. In addition, a counterexample with DKI < DSI is included, demonstrating that the relative efficiency of the two methods is problem-dependent rather than universal. The results show that for large-scale highly indeterminate frames, the graph-theoretic force method combined with WSA significantly reduces computational time while maintaining accuracy comparable to the displacement method. These findings highlight both the scalability and the limitations of the graph-theoretic force method, offering a balanced perspective for its practical application in structural optimization.

The transfer matrix method seen as one method of structural analysis among others

For the estimation of the strength of a structure, one could avoid detailed elastoplastic analysis and resort, instead, to direct limit analysis methods that are formulated within linear programming. This work describes the application of the force method to the limit analysis of three-dimensional frames. For the limit analysis of a framed structure, the force method, being an equilibrium-based approach, is better suited than the displacement method and results, generally, to faster solutions. Nevertheless, the latter has been used mostly, since it has a better potential for automation. The difficulty for the direct computerization of the force method is to automatically pick up the structure’s redundant forces. Graph theory concepts may be used to accomplish this task, and a numerical procedure was proposed for the optimal plastic design of plane frames. An analogous approach is developed herein for the limit analysis of space frames which is computationally more cumbersome than the limit analysis of plane frames. The proposed procedure results in hypersparse matrices, and in conjunction with the kinematic upper bound linear program which is solved by a sparse solver, the proposed method appears computationally very efficient. It is also proved that it is much more effective than any displacement-based formulation. The robustness and efficiency of the approach are testified by numerical examples for grillages and multi-storey frames that are included.

Steel Thin-walled Beams with restrained flanges are commonly used in structural systems where partial or full lateral and rotational restraints may occur, such as in steel–concrete composite beams used in slabs and in highway bridge decks. While these restraints enhance global stability, they can also trigger complex buckling behaviours. One such mode is lateral-distortional buckling (LDB), which arises when the tension flange is restrained against both lateral translation and rotation, leading to web distortion and twisting of the compression flange during buckling. Numerous studies have shown that existing empirical methods for predicting the elastic critical moment of LDB lack sufficient accuracy. This paper presents a numerical approach for estimating the elastic lateral and distortional buckling capacity of thin-walled I-beams under uniformly distributed loading. The developed method, referred to as Distortional Beam Formulations (DBF13), offers an efficient and practical modeling framework that incorporates second-order shell kinematics to accurately capture LDB behaviour. To validate the proposed formulation, Shell-element models were used in case studies and compared against existing experimental and analytical data. A total of 3540 analyses were conducted on doubly-symmetric and mono-symmetric I-section models under various boundary conditions to evaluate DBF13 across different buckling scenarios. Additionally, the effects of the cross-section classification, beam span, flange and web slenderness ratios were examined. The case study results underscore the reliability of DBF13 in predicting the Lateral Torsional Buckling as well as the Lateral Distortional Buckling behaviour. In the eigenvalue predictions, DBF13 has shown an average difference of less than 11% compared to shell model results.

Numerical analysis of interface damage in ballastless track on simply supported bridge due to thermal and vehicle dynamic load

In a large class of dynamic problems occurring in nuclear reactor safety analysis, the forcing function is derived from the fluid enclosed within the structure itself. Since the structural displacement depends on the fluid pressure, which in turn depends on the structural boundaries, a rigorous approach to this class of problems involves simultaneous solution of the coupled fluid mechanics and structural dynamics equations with the structural response and the fluid pressure as unknowns. Such an approach requires that the computer codes used to derive the forcing function and to analyze the structural response be radically modified or even abandoned. This paper offers an alternate approach to the foregoing problems. It is shown that for this kind of problem, the effect of fluid-structure interaction can be accounted for by a fluid mass matrix, which can be computed by the series expansion method. The advantage of this approach is that neither the computer code used to calculate the forcing function nor the ones for structural dynamics analysis need be modified. In fact, once the proper fluid mass matrix is computed, the problem can be solved by ordinary methods of structural dynamic analysis. Furthermore, since the fluid mass matrix is computed by a series expansion method, interfacing with a finite-element structural analysis computer code is relatively simple. On the other hand, the technique is restricted to small structural displacement with cylindrically symmetric fluid-structure boundaries. In addition, the fluid must be single phase.

A distributed inelasticity cyclic model of reinforced concrete (RC) columns is developed, using as a building block the tangent flexibility matrix of a section, which relates the three nondimensional normal stress resultants to the three corresponding section deformations. It is given in a companion paper in terms of the amount and distribution of the column longitudinal and transverse reinforcement. The tangent flexibility matrix of the cross section is integrated numerically along the element length to give the tangent flexibility (and stiffness, by inversion) matrix of slender reinforced concrete columns, in which flexure dominates the cyclic inelastic behavior. The model is implemented into a finite element program for the nonlinear static or dynamic analysis of structures in three dimensions. The program is applied to predict the results of cyclic uniaxial or biaxial tests, as well as the dynamic response of an actual reinforced concrete building to the three components of the Kalamata 1986 earthquake. The model predictions are in good agreement with the test results and with the damage inflicted to the building by the earthquake.

Non-convergence often occurs in the solution of highly nonlinear problem by conventional implicit finite element method. As another choice, explicit method is sometimes used by researchers. Through 2 typical static and dynamic examples this paper verifies that explicit finite element method can provide the same exactness of calculation as the implicit method even in the situation that the duration of action exceeds the natural period of structure greatly. At the same time, compared with implicit method, explicit method possesses higher speed, more robust algorithm, and stronger nonlinear capability, so that explicit method can be applied in static and dynamic analysis of structures, especially in large deformation and highly nonlinear problem.

This chapter presents the static and dynamic analysis of structures with uncertain parameters using fuzzy finite element method. Uncertainties presents in the parameters are modelled through convex normalised fuzzy sets. Fuzzy finite element method converts the structures into fuzzy system of linear equations and fuzzy eigenvalue problem for static and dynamic problems respectively. As such method to solve fuzzy system of linear equations, fully fuzzy system of linear equations and fuzzy eigenvalue problems are presented. These methods are applied to various structural problems to find out the fuzzy static and dynamic responses of the structures. Also the chapter analyses the numerical solution of uncertain fractionally damped spring-mass system. Uncertainties considered in the initial condition of the system.