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A simple estimate of the accuracy of the widely‐used Geckeler approximation for the axisymmetric bending of non‐shallow spherical shells is presented. Based on the edge‐deformation coefficients associated with a pair of arbitrary edge loadings, this estimate is independent of the actual surface‐loading and edge conditions of a practical shell. In this respect, the note complements the findings of an earlier error study, which was based on specific surface loadings and boundary conditions. The complementary nature of the work lies in its use for providing (in the absence of more specialised results) a reasonable assessment of the accuracy of the Geckeler approximation for any loading and/or boundary conditions.

The accuracy of the bending disturbances in (axisymmetrically loaded) spherical shells is computed by means of the widely used simplified method known as Geckeler's approximation (often employed as a benchmark for numerical models). The study is based on a comparison between Geckeler's approach and a related, but ‘superior’ approximation which, for practical purposes, may be considered to be exact. Conclusions are drawn from the results of a parametric investigation that encompasses various loading types, boundary conditions and shell geometries (i.e. springing angles and slenderness ratios).

In the analysis of some near‐regular structures one can solve the regular part independently and then superimpose the effect of the additional part. For such models, the matrices corresponding to regular part have canonical forms and their eigensolution or inversion can easily be performed. The effect of member changing the regular to a near‐regular structure can then be added. The purpose of this paper is to analyze near‐regular structures using the force method.

The paper uses the force method, and instead of selecting a statically determinate basic structure (standard method), the paper employs the regular part of the structure as the basic structure.

A new algebraic method is introduced for the force method of analysis for efficient analysis of large near‐regular structures.

In this paper, the force method is used, however, instead of selecting a statically determinate basic structure, the regular part of the structure is employed as the basic structure. Those additional elements are considered as redundant elements. This method is applied to truss and frame structures. In the present approach it is possible to have missing elements instead of additional elements.

The purpose of this paper is to propose a numerical prediction method of buckling loads for shell structures under axial compression and thermal loads based on vibration correlation technique (VCT).

VCT is a non-destructive test method, and the numerical realization of its experimental process can become a promising buckling load prediction method, namely numerical VCT (NVCT). First, the derivation of the VCT formula for thin-walled structures under combined axial compression and thermal loads is presented. Then, on the basis of typical NVCT, an adaptive step-size NVCT (AS-NVCT) calculation scheme based on an adaptive increment control strategy is proposed. Finally, according to the independence of repeated frequency analysis, a concurrent computing framework of AS-NVCT is established to improve efficiency.

Four analytical examples and one optimization example for imperfect conical-cylindrical shells are carried out. The buckling prediction results for AS-NVCT agree well with the test results, and the efficiency is significantly higher than that of typical numerical buckling methods.

The derivation of the VCT formula for thin-walled shells provides a theoretical basis for NVCT. The adaptive incremental control strategy realizes the adaptive adjustment of the loading step size and the maximum applied load of NVCT with Python script, thus establishing AS-NVCT.

The purpose of this paper is to describe how the method recently developed for mass‐spring systems and frame structures is modified to include the free vibration of trusses.

Here, two methods are presented for calculating the eigenfrequencies of structures. The first approach is graph theoretical and uses graph symmetry. The graph models are decomposed into submodels and healing processes are employed such that the union of the eigenvalues of the healed submodels contain the eigenvalues of the entire model. The second method has an algebraic nature and uses special canonical forms. The present method is illustrated through three simple examples with odd and even number of bays.

The inter‐relation for the mechanical properties of elements is established using new weighted graphs, enabling easy calculation of the eigenvalues involved. Two methods are presented for calculating the eigenfrequencies of the truss structures.

Symmetry is used for easy calculation of the eigenfrequencies of structures.

There are many structures that have a repetitive pattern. If a relationship can be established between a repetitive structure and a circulant structure, then the repetitive structure can be analyzed by using the properties of the corresponding circulant structure. The purpose of this paper is to develop such a transformation.

A circulant matrix has certain properties that can be used to reduce the complexity of the analysis. In this paper, repetitive and near-repetitive structures are transformed to circulant structures by adding and/or eliminating some elements of the structure. Numerical examples are provided to show the efficiency of the present method.

A transformation is established between a repetitive structure and a circulant structure, and the analysis of the repetitive structure is performed by using the properties of the corresponding circulant structure.

Repetitive and near-repetitive structures are transformed to circulant structures, and the complexity of the analysis of the former structures is reduced by analyzing the latter structures.

The purpose of this paper is to present an efficient method for dynamic analysis of structures utilizing a modal analysis with the main purpose of decreasing the computational complexity of the problem. In traditional methods, the solution of initial-value problems (IVPs) using numerical methods like finite difference method leads to step by step and time-consuming recursive solutions.

The present method is based on converting the IVP into boundary-value problems (BVPs) and utilizing the features of the latter problems in efficient solution of the former ones. Finite difference formulation of BVPs leads to matrices with repetitive tri-diagonal and block tri-diagonal patterns wherein the eigensolution and matrix inversion are obtained using graph products rules. To get advantage of these efficient solutions for IVPs like the dynamic analysis of single DOF systems, IVPs are converted to boundary-value ones using mathematical manipulations. The obtained formulation is then generalized to the multi DOF systems by utilizing modal analysis.

Applying the method to the modal analysis leads to a simple and efficient formulation. The laborious matrix inversion and eigensolution operations, of computational complexities of O(n2.373) and O(n3), respectively, are converted to a closed-form formulation with summation operations.

No limitation.

Swift analysis has become possible.

Suitability of solving IVPs and modal analysis using conversion and graph product rules is presented and applied to efficient seismic optimal analysis and preliminary design.

In this paper, the authors aim to examine and comparatively evaluate a recently-developed metaheuristic called crystal structure algorithm (CryStAl) – which is inspired by the symmetries in the internal structure of crystalline solids – in solving engineering mechanics and design problems.

A total number of 20 benchmark mathematical functions are employed as test functions to evaluate the overall performance of the proposed method in handling various functions. Moreover, different classical and modern metaheuristic algorithms are selected from the optimization literature for a comparative evaluation of the performance of the proposed approach. Furthermore, five well-known mechanical design examples are utilized to examine the capability of the proposed method in dealing with challenging optimization problems.

The results of this study indicated that, in most cases, CryStAl produced more accurate outputs when compared to the other metaheuristics examined as competitors.

This paper can provide motivation and justification for the application of CryStAl to solve more complex problems in engineering design and mechanics, as well as in other branches of engineering.

CryStAl is one of the newest metaheuristic algorithms, the mathematical details of which were recently introduced and published. This is the first time that this algorithm is applied to solving engineering mechanics and design problems.