Stability of orthotropic elastic–plastic open conical shells

The paper presents a derivation of the stability equation and the solution method of the problem for an orthotropic elastic–plastic open conical shell. The use is made of the constitutive relations of incremental plastic flow theory, elastic compressibility of the material, and Shanley concept of increasing load are taken into account in the consideration. A variation, strain energy method is used to derive the stability equation for bilayered open conical shell with nonuniform pre-critical stress distribution. The shell is free supported at the edges and the load acting the shell, in the form of longitudinal force and lateral pressure, is active one, i.e. unloading is not considered.     

An elastic–plastic analysis of large deflection of thin shell structure using a delta-sequence function

The analysis of thin shell under large deflection has complex problem associated with the geometrical and material nonlinearities, in which the solutions for stress and deformation are desired to obtain the same level accuracy. One of ordinary and powerful method for this subject is a finite element method that has generally inconvenience to be necessarily extensive calculation due to large number of freedom.This paper is concerned with the elastic–plastic analysis of thin shell structures by the hybrid method using a functional for the principle of modified complementary energy. For elastic–plastic materials, the numerical calculation could be well executed by the way that the stress distribution across the panel thickness is expressed as continuous function using the delta-sequence function. This approach introduces a considerable way for the reduction of computing volume. The proposed method was applied to discuss the resisting mechanism of thin shell structure under large deflection.     

Stability of elastic–plastic conical shells under shear loading

A method of determination of critical loads for thin-walled conical shells loaded by shear forces developed by moment of twist is presented. The three governing equations of neutral equilibrium with respect to basic displacement vector components u, v, and w are used. It is assumed that effective stress in the prebuckling state of stress in the shell can exceed the yield limit of the shell material. The use is made both of physical relations of Nadai–Hencky small elastic–plastic deformation theory of plasticity, and Prandtl–Reuss J₂ incremental plastic flow theory. Also, a bilinear stress–strain material model, material compressibility and Shanley approach will be accepted in the analysis. Galerkin method is applied to solve the problem equations and iterative techniques are accepted in numerical algorithm to determine critical loads for elastic–plastic shells.     

Analytical solution for a circular opening in an elastic–brittle–plastic rock

This paper deals with the analytical solutions for the prediction of displacements around a circular opening in an elastic–brittle–plastic rock mass compatible with a linear Mohr–Coulomb or a nonlinear Hoek–Brown yield criterion. Three different cases of definitions for elastic strains in the plastic region, used in the existing solutions, are mentioned. The closed-form analytical solutions for the displacement in the plastic region are derived on a theoretically consistent way for all the cases by employing a non-associated flow rule. The results of the dimensionless displacements are compared using the data of the soft and hard rocks to investigate the effect of different definitions for elastic strains with the dilation angle.     

A semi-analytical method for the elastic–plastic large deflection analysis of stiffened panels under combined biaxial compression/tension, biaxial in-plane bending, edge shear, and lateral pressure loads

In the earlier publications [Paik JK, Thayamballi AK, Lee SK, Kang SJ. A semi-analytical method for the elastic-plastic large deflection analysis of welded steel or aluminium plating under combined in-plane and lateral pressure loads. Thin-Walled Struct 2001;39;125–52; Paik JK, Thayamballi AK. Ultimate limit state design of steel-plated structures. Chichester: Wiley; January 2003], the author presented a semi-analytical method for the elastic–plastic large deflection analysis of unstiffened plates under biaxial loads, edge shear, biaxial in-plane bending and out-of-plane (lateral) pressure loads until the ultimate strength is reached. In the present paper, a similar method is applied to stiffened panels subjected to the same type of loading. The effect of initial imperfections in the form of initial deflection and welding residual stresses is accounted for in the calculations. The validity of the developed method is demonstrated by comparing with existing theoretical and numerical results where relevant. The present theory can be useful for ultimate strength analysis of plates and stiffened panels made of steel or aluminium alloys.     

Elastic–brittle–plastic analysis of circular openings in Hoek–Brown media

A closed-form solution is presented in this paper for the prediction of displacements around circular openings in a brittle rock mass subject to a hydrostatic stress field. The rock mass is assumed to be governed by Hoek–Brown yield criterion and a non-associated flow rule is used. For the elastic–brittle–plastic analysis of circular openings in an infinite Hoek–Brown medium, the existing analytical solutions were found to be incorrect. The present closed-form solution is based on a theoretically consistent method and the solution does not require the use of any numerical method.The present closed-form solution was validated by using the finite element method. In the finite element analysis, the infinite boundary was simulated “exactly” by using the newly developed elastic support method. Several cases were analyzed and the present closed-form solutions for stresses and displacements were found to be in an excellent agreement with those obtained by using the finite element method.     

A systematic approach towards the structural behaviour of a lightweight deck–side shell system

Lightweight structures are increasingly used for high-speed ships. This paper presents a systematic approach to analyse the structural behaviour of a lightweight deck–side shell system using high strength steel. An analytical model of the deck–side shell system was first given, which includes the effects of stiffeners for the deck and side shell, the support conditions of the centreline girder (CL-girder), the influence of transverse beams, and the interaction between the side shell and the lightweight deck as parts of problems to the solution. By changing several geometric parameters, the sensitivity of both overall and local stress and deflection for the deck–side shell system was investigated. The different geometric parameters analysed comprise the influence for variation in the thickness of the web for transverse beams, longitudinal stiffeners and the CL-girder, the thickness of lower flange for the transverse beam and, the thickness for the panel. Furthermore, the influence of the lightweight deck and loads from the deck above on the side shell, the effects of the side shell and loads from top deck on the deck, the support conditions for the CL-girder, and the influence of deck loads on the eigenmodes were also analysed. By evaluating the results obtained from FE simulation, the support conditions of the CL-girder, the thickness of the panels and the lower flange of the transverse beams were found to be the most relevant parameters affecting both the stress and the deflection distribution of the structure. The dynamic characteristics of the structure were also analysed. The FE analysis concerning buckling of the structure was present. The results enable naval architects and structural engineers to design new extreme lightweight deck structure more reliable and economical. And some suggestions for future research are also given.     

Design and specification compilation of a modular‐prefabricated high‐rise steel frame structure with diagonal braces part II: Elastic–plastic time‐history analysis and joint design

The use of modular‐prefabricated steel structures has distinct advantages, such as rapid construction, industrial production, and environmental protection. Although this type of structure has been extensively employed around the world, it is primarily used for low‐rise buildings; its application in high‐rise buildings is limited. This paper proposes a new type of modular‐prefabricated high‐rise steel frame structure with diagonal braces. An elastic–plastic time‐history analysis of a 30‐storey building during rare earthquakes was performed. The base shear, storey drift, stress, damage characteristics, and other performances of the structure were investigated. According to the mechanism analysis, finite element simulation, and model test, the formulas for the elastic and elastic–plastic design of the truss–column connection, column–column flange connection, and diagonal brace–truss connection are proposed in this paper. The control parameters for the structural design are also discussed. This study provides an important reference for the research and design of this type of modular‐prefabricated high‐rise steel structure. The design method has been compiled into a design specification named Technical Specifications for Prefabricated Steel Frame Structure with Diagonal Bracing Joints, which is unique for this type of structure.     

Flexural–torsional behavior of thin-walled composite beams

This paper presents a flexural–torsional analysis of I-shaped laminated composite beams. A general analytical model applicable to thin-walled I-section composite beams subjected to vertical and torsional load is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional responses for arbitrary laminate stacking sequence configuration, i.e. unsymmetric as well as symmetric. Governing equations are derived from the principle of the stationary value of total potential energy. Numerical results are obtained for thin-walled composites under vertical and torsional loading, addressing the effects of fiber angle, and laminate stacking sequence.     

Prediction of cyclic freeze–thaw damage in concrete structures based on response surface method

The initiation and growth process of cyclic ice body in porous systems are affected by thermo-physical and mass transport properties as well as by gradients of temperature and chemical potentials. Furthermore, the diffusivity of deicing chemicals reaches a significantly higher value under cyclic freeze–thaw conditions. Moreover, disintegration of concrete structures is aggravated by marine environments, higher altitudes, and northern areas. A serious concern for concrete engineers is that the property of cyclic freeze–thaw with crack growth and the deterioration, caused by accumulated damages hard to be identified by testing. In order to predict the accumulated damages by cyclic freeze–thaw, an optimized regression analysis by response surface method (RSM) is performed. Such important parameters for cyclic freeze–thaw-deterioration of concrete structures as water to cement ratio, entrained air pores, and the number of cycles of freezing and thawing are used to construct the limit state function of RSM. The regression equation fitted to the important deterioration criteria such as accumulated plastic deformation, relative dynamic modulus and equivalent plastic deformations served as the probabilistic evaluation of the performance to resist the structural degradation. The prediction of relative dynamic modulus and residual strains after 300 cycles of freeze–thaw showed good agreements with the experimental results, showing that the RSM result can be used to predict the probability of failure for the accumulated damage by cyclic freeze–thaw using designer specified critical values. Hence, it is possible to evaluate the life cycle management of concrete structures by the proposed prediction method in consideration of the accumulated damage due to cyclic freeze–thaw.     

A semi-analytical method for the elastic-plastic large deflection analysis of welded steel or aluminum plating under combined in-plane and lateral pressure loads

The aim of the present paper is to develop a semi-analytical method which can quickly and accurately compute the elastic–plastic large deflection response of welded steel or aluminum plating under a combination of biaxial compression/tension, biaxial in-plane bending, edge shear and lateral pressure loads, until the ultimate limit state is reached. The post-weld initial imperfections (i.e. initial deflection and residual stresses) are included in the method as parameters of influence. It is assumed that the plating is simply supported at all (four) edges which are kept straight. A unique feature of the developed method is that geometric nonlinearity associated with large deflection response of plating under combined loads is treated by analytically solving the nonlinear governing differential equations of the elastic large deflection plate theory, while material nonlinearity due to plasticity is dealt with implicitly by a numerical procedure. This approach reduces the magnitude of numerical computations, resulting in a saving of modeling effort and computing time. As another contribution, this paper investigates and discusses the ultimate strength characteristics of plating, by varying the plate properties and load combinations, based on elastic–plastic large deflection analysis using the developed method.     

Shaking table test and theoretical analysis of the pile–soil–structure interaction at a liquefiable site

Pile foundations are widely used to support high‐rise buildings, in which piles transmit foundation loads to soil strata with higher bearing capacity and stiffness. This process alters the dynamic characteristics of the pile–soil–structure system in seismically active areas, especially at a liquefiable site. A series of shaking table tests on liquefiable soils in pile group foundations of tall buildings were performed to evaluate the liquefaction process and dynamic responses of the pile, soil, and structure. The soil was composed of two layers: the upper layer was a clay layer and the lower layer was saturated sand. These layers were placed in a flexible container that was excited by El Centro earthquake events and Shanghai Bedrock waves at different levels. The test results indicate that the pore pressure ratio is gradually enhanced as the amplitude of the input acceleration increases. The liquefied sand has a filtering effect on the vibration with a high frequency and an amplified effect on the vibration with a low frequency. With increased excitation, contact pressure and strain amplitudes of the pile increase, whereas the peak acceleration magnification coefficient decreases. The seismic responses of a structure with pile–soil–structure interaction are generally smaller than those on a rigid foundation.     

Influence of the depth and shape of a tunnel in the application of the convergence–confinement method

One of the most widely used methods in tunnel support analysis and design is the convergence–confinement method (CCM). For its practical application, it is necessary to study the influence of the depth and cross-section of the tunnel and to confirm the calculations with two- or three-dimensional simulations carried out with finite elements or explicit finite differences programs. These simulations require elevated calculation times. In this paper, a modification of the CCM is proposed that directly introduces the effect of depth and the shape of the tunnel cross-section in the determination of the radial displacement of the tunnel. To do so, a series of functions are determined that approximate the radial displacement at points situated on the perimeter of the cross-section of the tunnel, considering several cross-sections at different distances from the working face. Should the cross-section of the tunnel or its depth be modified, it will not be necessary to perform new numerical simulations in order to apply the CCM. It will only be necessary to use the calculated shape functions. It is thus possible to use the CCM in the analysis and design of the support elements in a quite precise and significantly faster way.     

Improvement in accuracy of the finite element method in analysis of stability of Euler–Bernoulli and Timoshenko beams

The problem of buckling of the Euler–Bernoulli and Timoshenko beams is analyzed by the finite element method. Significant improvement in accuracy of the method is obtained by replacing the discontinuous function of the bending moment related to the approximation of the eigenfunction obtained by FEM by a “smoothed” function in the Rayleigh quotient. The smoothed function is obtained by fitting the discontinuous one using the least square technique.     

A beam model for the flexural–torsional buckling of thin-walled members with some applications

A beam model aimed at describing the flexural–torsional buckling of thin-walled members with non-symmetric cross-sections is presented. Two beam axes are introduced, and strain is defined with respect to both. The shearing strain between the cross-section and one of the two axes is assumed to vanish; the warping is supposed to be linear in the twist. Non-linear hyperelastic constitutive relations are introduced; by means of standard localization and static perturbation techniques, the field equations describing the flexural–torsional buckling are obtained. One benchmark example is given and some numerical values of the critical load for various warping constraints at the beam ends are provided.     

An adaptive numerical scheme based on the Craig–Bampton method for the dynamic analysis of tall buildings

A new numerical scheme is proposed to perform a nonlinear dynamic analysis for tall buildings. The structural components (beams and columns) of tall buildings gradually enter the inelastic phase under strong seismic excitation. Because the distribution of nonlinear components is initially unknown due to the randomness of earthquake inputs, a group of linear and nonlinear substructures are automatically figured out during the time‐history analysis of a structure. Then a modified Craig–Bampton method is proposed to condense the DOFs of the linear substructures in modal coordinates at each time step while keeping the governing equation of the nonlinear substructure in physical coordinates. The dominant modes of the linear substructures are selected to capture the main dynamic characteristics of the structure. The time step integration analysis is used to solve the governing equation of the structures in hybrid coordinates. A 20‐story building is employed as the numerical simulation test to validate the feasibility and effectiveness of the proposed numerical scheme. This scheme provides a new method for the nonlinear dynamic analysis of tall buildings with acceptable simulation accuracy and high computational efficiency.     

Effects of soil on the energy response of equipment–structure systems with different connection types between the equipment and structure

In equipment–structure systems, the soil–structure interaction and connection types between the equipment and structure significantly affect the seismic response. To understand this effect, in this study, the motion equation of an equipment–structure–soil system was derived, and energy balance equations for each part of the coupled system were obtained. Further, the effects of the soil on the energy response were analyzed based on the results of shaking table tests of an equipment–structure system and real‐time substructure shaking table tests of equipment–structure–soil systems with different connection types. The energy response of the equipment–structure system with a rigid ground was compared with that of the equipment–structure–soil systems. The analysis results showed that the energy response of the equipment–structure–soil system with different connections was quite different from that of the system with a rigid ground. The soil decreased the total energy input to the equipment and structure and significantly changed the time distribution characteristics of the input energy. Additionally, the soil weakened the energy consumption of the connections. Therefore, the influence of the soil should be considered in the design of equipment–structure systems with connections.     

Cost–benefit analysis of constructing a filtration plant for the National Water Carrier in Israel

The paper presents an economic cost–benefit analysis (CBA) of the construction of a filtration plant for the Israeli National Water Carrier (NWC). Its main contribution lies in the comparison between the costs and the benefits of filtration in the context of a concrete policy choice. The first part of the paper presents a cost analysis of two alternative engineering systems: central filtration and localized filtration. The analysis shows that the costs of constructing and operating a central filtration plant are significantly lower than those of a system of local plants. The second part of the paper presents a two‐stage method for assessing the benefits of filtration. First, we valuate the damages caused by consumption of unfiltered water; then we estimate consumers' willingness to pay (WTP) for improved water quality, taking into account households' potential risk aversion. The main result is that total WTP significantly outweighs the costs of constructing and operating the plant.     

End bearing capacity of a single incompletely end-supported pile based on the rigid plastic finite element method with non-linear strength property against confining stress

An Incompletely End Supported Pile (IESP) is a pile in a soft soil layer underlain by a hard soil layer that does not reach the bottom hard layer in practice. This study estimates the end bearing capacity of IESP by using an inhouse Rigid Plastic FEM code (RPFEM), considering shear strength non-linearity of soil against confining pressure, and soil-foundation interaction. The effect of the distance between the pile tip and the bottom hard soil layer (d/B) on the end-bearing capacity of IESP was mainly investigated for three types of soil: cohesive soils, cohesionless soils and intermediate soils. Also, theratio (r) of the end bearing capacity of the pile when it reaches the bottom hard layer to that of the pile when the bottom layer has no influence was was considered. By considering the shear strength non-linearity, the end bearing capacity was accurately estimated. The estimations were consistent with previous analytical, experimental and numerical solutions. It is found that the end bearing capacity inversely decreases with the distance d/B and becomes constant around d/B = 3. Based on the results, a formula for estimating the end bearing capacity of IESP is proposed. Comparisons with methods in existing literature confirmed the reliability of the proposed equation.     

Study on the damage propagation of surrounding rock from a cold-region tunnel under freeze–thaw cycle condition

Using an equipment with CT (computerized tomography), the characteristics of damage propagation of rock from a cold-region tunnel were studied under different conditions with freeze–thaw cycles, and the results were described by CT images and CT values. The relationships between damage development and the amount of water-supply, and loading or unloading process were also discussed during the repeated freeze–thaw, respectively, as well as the intensity change; moreover, the rate of breakage was also put forward. It was shown that the CT values and CT images could directly express the damage situation of rock, and the results were expected to provide a referenced basis for numerical computation and the safe running of cold-region tunnel.