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This paper presents the generalized theory of the most important energy principles in structural analysis. All derive from two basic complementary theorems denoted as the principles of virtual displacements and virtual forces. Both exact and approximate methods are discussed and particular attention is paid to the derivation of upper and lower limits. The theory is not restricted to linearly elastic bodies but includes ab initio the effect of non‐linear stress‐strain laws and thermal strains. Finally the basic principles are illustrated on a number of simple examples in preparation for the more complex ones to appear in Parts II and III.

This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic model with an arbitrary number of parallel units is used for treating the relaxation. Each unit has one dashpot and two springs. A stress-strain-time relationship is derived for the case when the coefficient of viscosity in each unit of the viscoelastic model changes continuously with time. The beam exhibits continuous material inhomogeneity along the thickness. Thus, the moduli of elasticity and the coefficients of viscosity vary continuously in the thickness direction. The aim of the present paper is to obtain time-dependent solutions to the strain energy release rate that take into account the relaxation when the coefficient of viscosity changes with time.

Time-dependent solutions to the strain energy release rate are derived by considering the time-dependent strain energy and also by using the compliance method. The two solutions produce identical results.

The variation of the strain energy release rate with time due to the relaxation is analysed. The influence of material inhomogeneity and the crack location along the beam width on the strain energy release rate are evaluated. The effects of change of the coefficients of viscosity with time and the number of units in the viscoelastic model on the strain energy release rate are assessed by applying the solutions derived.

The time-dependent strain energy release rate for a longitudinal vertical crack in a beam under relaxation is analysed for the case when the coefficients of viscosity change with time.

In this paper, the peak kinetic energy density (KED) of soil particles during earthquake excitation is used as an intensity measure for the evaluation of liquefaction potential under field conditions. The paper seeks to discuss this measure.

Using centrifuge tests data, it is shown that seismic pore water pressure buildup is proportional to cumulative KED at a particular soil depth. Linear relationships are found between cumulative kinetic energy and corresponding cumulative strain energy. To consider the effect of soil amplification, several equivalent linear ground response analyses are performed and the results are used to derive an equation for depth reduction factor of peak kinetic energy density. Two separate databases of liquefaction case histories are used in order to validate the proposed model. The performance of the proposed model is compared with a number of commonly used shear stress‐based liquefaction assessment methods. Finally, the logistic regression method is employed to obtain probabilistic boundary curves based on the present model. Parametric study of the proposed probabilistic model is carried out to verify its agreement with the previous methods.

It has been shown that the kinetic energy model works satisfactorily in classifying liquefied and non‐liquefied cases compared with the existing recommendations of shear stress‐based criterion. The results of the probabilistic kinetic energy model are in good agreement with those of previous studies and show a reasonable trend with respect to the variations of fines content and effective overburden pressure. The proposed model can be as used an alternative approach for assessment of liquefaction potential.

These findings make a sound basis for the development of a kinetic energy‐based method for assessment of liquefaction potential.

In pure material design, the previous research has indicated that lots of optimization factors such as used algorithm and parameters have influence on the optimal solution. In other words, there are multiple local minima for the topological design of materials for extreme properties. Therefore, the purpose of this study is to attempt different or more concise algorithms to find much wider possible solutions to material design. As for the design of material microstructures for macro-structural performance, the previous studies test algorithms on 2D porous or composite materials only, it should be demonstrated for 3D problems to reveal numerical and computational performance of the used algorithm.

The presented paper is an attempt to use the strain energy method and the bi-directional evolutionary structural optimization (BESO) algorithm to tailor material microstructures so as to find the optimal topology with the selected objective functions. The adoption of the strain energy-based approach instead of the homogenization method significantly simplifies the numerical implementation. The BESO approach is well suited to the optimal design of porous materials, and the generated topology structures are described clearly which makes manufacturing easy.

As a result, the presented method shows high stability during the optimization process and requires little iterations for convergence. A number of interesting and valid material microstructures are obtained which verify the effectiveness of the proposed optimization algorithm. The numerical examples adequately consider effects of initial guesses of the representative unit cell (RUC) and of the volume constraints of solid materials on the final design. The presented paper also reveals that the optimized microstructure obtained from pure material design is not the optimal solution any more when considering the specific macro-structural performance. The optimal result depends on various effects such as the initial guess of RUC and the size dimension of the macrostructure itself.

This paper presents a new topology optimization method for the optimal design of 2D and 3D porous materials for extreme elastic properties and macro-structural performance. Unlike previous studies, the presented paper tests the proposed optimization algorithm for not only 2D porous material design but also 3D topology optimization to reveal numerical and computational performance of the used algorithm. In addition, some new and interesting material microstructural topologies have been obtained to provide wider possible solutions to the material design.

This study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C¹ basis functions for the crack evolution scalar field in a finite element framework. To address this, non-Sibsonian type shape functions that are nonpolynomial types based on distance measures, are used in the context of natural neighbor shape functions. The capability and efficiency of this method are studied for modeling cracks.

The weak form of the fourth-order PFM is derived from two governing equations for finite element modeling. C⁰ non-Sibsonian shape functions are derived using distance measures on a generalized quad element. Then these shape functions are degree elevated with Bernstein-Bezier (BB) patch to get higher-order continuity (C¹) in the shape function. The quad element is divided into several background triangular elements to apply the Gauss-quadrature rule for numerical integration. Both fourth-order and second-order PFMs are implemented in a finite element framework. The efficiency of the interpolation function is studied in terms of convergence and accuracy for capturing crack topology in the fourth-order PFM.

It is observed that fourth-order PFM has higher accuracy and convergence than second-order PFM using non-Sibsonian type interpolants. The former predicts higher failure loads and failure displacements compared to the second-order model due to the addition of higher-order terms in the energy equation. The fracture pattern is realistic when only the tensile part of the strain energy is taken for fracture evolution. The fracture pattern is also observed in the compressive region when both tensile and compressive energy for crack evolution are taken into account, which is unrealistic. Length scale has a certain specific effect on the failure load of the specimen.

Fourth-order PFM is implemented using C¹ non-Sibsonian type of shape functions. The derivation and implementation are carried out for both the second-order and fourth-order PFM. The length scale effect on both models is shown. The better accuracy and convergence rate of the fourth-order PFM over second-order PFM are studied using the current approach. The critical difference between the isotropic phase field and the hybrid phase field approach is also presented to showcase the importance of strain energy decomposition in PFM.

A DSIR Sponsored Research Programme on the Development and Application of the Matrix Force Method and the Digital Computer. This work presents a rational method for the structural analysis of stressed skin fuselages for application in conjunction with the digital computer. The theory is a development of the matrix force method which permits a close integration of the analysis and the programming for a computer operating with a matrix interpretive scheme. The structural geometry covered by the analysis is sufficiently arbitrary to include most cases encountered in practice, and allows for non‐conical taper, double‐cell cross‐sections and doubly connected rings. An attempt has been made to produce a highly standardized procedure requiring as input information only the simplest geometrical and elastic data. An essential feature is the use of the elimination and modification technique subsequent to the main analysis of the regularized structure in which all cutouts have been filled in. Current Summary A critical historical appraisal of previous work in the Western World on fuselage analysis is given in the present issue together with an outline of the ideas underlying the new theory.

THE methods of wing stress analysis at present in use have in most cases been developed on the assumptions that the ribs are rigid in their own planes, and that they may be considered equivalent to an infinite number of infinitely thin ribs, infinitely closely spaced. The problem may then be treated by the methods of the calculus, as was done, for example, in an article by the writer in AIRCRAFT ENGINEERING, January and February, 1943. A more recent and much more comprehensive paper on the same subject has been published by J. Hadji‐Argyris and P. C. Dunne in the R. Ac. Society Journal, February, September and November, 1947, and May and June, 1949.

THE efficient design and construction of the latest types of Swedish military aircraft, with wings with high critical Mach numbers, has necessitated a thorough investigation into the structural behaviour of swept and delta wings of both the thin and thick types. It is the main purpose of this paper to present some important test results and pertinent details of some of the small scale models which have been built to supplement the theoretical estimation of the stress distribution and deflexion patterns. In some cases these models have also been constructed to provide information on certain unusual structural configurations, which would have otherwise taken many months to obtain by using approximate theoretical methods. The stress distributions for each model are illustrated in such a way that comparison between the different types of structures may readily be made.

The strain energy method for the analysis of pin‐jointed redundant frameworks is expressed in matrix form suitable for solution on electronic computers. This is illustrated by its application to a zero‐length launcher framework having sixty‐three members, nine of which are redundant, using the Ferranti Pegasus computer. It is concluded that a framework must be reasonably complex before the use of this method is justified but that problems of greater complexity than would normally be attempted can readily be solved.

This paper aims to establish a more accurate model for lifetime estimation.

Finite element model simulation and experimental tests are used to enhance the lifetime prediction model of the solder joint.

A more precise model was found.

It is confirmed that the paper is original.