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Current procedures of buckling load estimation for thin-walled structures may provide very conservative estimates. Their refinement offers the potential to use structure and material properties more efficiently. Due to the large variety of design variables, for example laminate layup in composite structures, a prohibitively large number of tests would be required for experimental assessment, and thus reliable numerical techniques are of particular interest. The purpose of this paper is to analyze different methods of numerical buckling load estimation, formulate simulation procedures suitable for commercial software and give recommendations regarding their application. All investigations have been carried out for cylindrical composite shells; however similar approaches are feasible for other structures as well.

The authors develop a concept to apply artificial load imperfections with the aim to estimate as good as possible lower bounds for the buckling loads of shells for which the actual physical imperfections are not known. Single and triple perturbation load approach, global and local dynamic perturbation approach and path following techniques are applied to the analysis of a cylindrical composite shell with known buckling characteristics. Results of simulations are compared with published experimental data.

A single perturbation load approach is reproduced and modified. Buckling behavior for negative values of the perturbation load is examined and a pattern similar to a positive perturbation load is observed. Simulations with three perturbation forces show a decreased (i. e. more critical) value of the buckling load compared to the single perturbation load approach. Global and local dynamic perturbation approaches exhibit a behavior suitable for lower bound estimation for structures with arbitrary geometries.

Various load imperfection approaches to buckling load estimation are validated and compared. All investigated methods do not require knowledge of the real geometrical imperfections of the structure. Simulations were performed using a commercial finite element code. Investigations of sensitivity with respect to a single perturbation load are extended to the negative range of the perturbation load amplitude. A specific pattern for a global perturbation approach was developed, and based on it a novel simulation procedure is proposed.

We present a qualitative analysis of the fundamental static semiconductor device equations which is based on singular perturbation theory. By appropriate scaling the semiconductor device equations are reformulated as singularly perturbed elliptic system (the Laplacian in Poisson's equation is multiplied by a small parameter ?2, the so‐called singular perturbation parameter). Physically the singular perturbation parameter is identified with the square of the normed minimal Debye length of the device under consideration. Using matched asymptotic expansions for small A we characterize the behaviour of the solutions locally at pn junctions, Schottky contacts and oxide‐semiconductor interfaces and demonstrate the occurrence of exponential internal/boundary layers at these surfaces. The derivatives of the solutions blow up within these layer regions (as ?2 decreases) and they remain bounded away from the layers. We demonstrate that the solutions of the ‘zero‐space charge approximation’ are close to the solutions of the ‘full’ semiconductor problem (when ? is small) away from layer regions and derive a second‐order ordinary differential equation which (when subjected to appropriate boundary/interface conditions) ‘describes’ the solutions within layer regions.

The concept of vulnerability in climate change literature is underpinned by numerous theoretical contributions across different disciplines leading to disparate understandings of what climate change vulnerability entails, as well as different methodological frameworks for assessment. This multiplicity of contributions helped not only to frame and shape different understandings of vulnerability but also to define the conceptual and analytical elements considered as critical in any climate change vulnerability assessment. The purpose of this paper is to review the literature on climate change vulnerability and explore and synthesize those conceptual and analytical aspects considered fundamental in a vulnerability assessment in climate change.

Drawing on existing literature on climate change vulnerability and vulnerability assessment frameworks, the paper provides a review of the conceptual elements regarded as critical in integrated assessments of climate change vulnerability to date.

A review of the existing literature identified nine critical elements in vulnerability assessments: the coupled human-environment system and place-based analysis; key components of vulnerability; multiple perturbations; scales of analysis; causal structures of vulnerability; engaging stakeholders; differential vulnerability; historical and prospective analysis; and dealing with uncertainty. The paper concludes by highlighting some of the remaining challenges and limitations for the development of integrated vulnerability assessment in climate change research.

The paper presents a synthesis that draws on existing literature on climate change vulnerability theory, as well as vulnerability assessment frameworks that attempt to apply those concepts in the assessment of climate change vulnerability.

This paper aims to propose a simplified model of vanadium redox flow batteries (VRBs) for VRB energy storage system (ESS) design considering the operational characteristics of VRB, and a VRB ESS, considering the low terminal voltage of VRB, was presented.

According to the designed topology of VRB ESS and the simplified model of VRB, a small perturbation analysis method was used to establish the transfer function of VRB ESS, and the controller parameters of VRB ESS under constant charging and discharging current were designed.

Test results have demonstrated that this designed VRB ESS has fast response, small overshoot, strong adaptation and high steady precision, which strongly verified the reasonable design.

This simplified model of VRB can be suitably used for VRB ESS design. This designed VRB ESS realized the bidirectional power flow of VRB and AC grid. In this designed VRB ESS, phase-shifted full-bridge converter and a single-phase inverter were used and VRB was charged and discharged under constant current.

The paper presents a topology of VRB ESS which can realize the bidirectional power flow of VRB and AC grid. Considering the complexity of VRB model, a simplified model of VRB was proposed for the controller parameters design of VRB ESS, and this method can be used in application.

The paper focuses on the solution of a numerical model to explore the sliding and non‐Newtonian fluid behaviour in soft elastohydrodynamic nip contacts. The solution required the coupling of the fluid and elastomer regimes, with the non‐Newtonian fluid properties being described using a power law relationship. The analysis showed that the fluid characteristics as defined by the power law relationship led to large differences in the film thickness and flow rate with a movement of the peak pressure within the nip contact. The viscosity coefficient, power law index and sliding ratio were shown to affect the nip performance in a non‐linear manner in terms of flow rate and film thickness. This was found to be controlled principally by the level of viscosity defined by the power law equation. The use of a speed differential to control nip pumping capacity was also explored and this was found to be most sensitive at lower entrainment speeds.

To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

The methodology is based on an n‐th order expansion (perturbation) for input random parameters and state functions around their expected value to recover probabilistic moments of the response. A finite element formulation permits stochastic simulations on irregular meshes for practical applications.

The methodology permits approximation of expected values and covariances of quantities such as the fluid pressure and flow velocity using both symbolic and discrete FEM computations. It is applied to inviscid irrotational flow, Poiseulle flow and viscous Couette flow with randomly perturbed boundary conditions, channel height and fluid viscosity to illustrate the scheme.

The focus of the present work is on the basic concepts as a foundation for extension to engineering applications. The formulation for the viscous incompressible problem can be implemented by extending a 3D viscous primitive variable finite element code as outlined in the paper. For the case where the physical parameters are temperature dependent this will necessitate solution of highly non‐linear stochastic differential equations.

Techniques presented here provide an efficient approach for numerical analyses of heat transfer and fluid flow problems, where input design parameters and/or physical quantities may have small random fluctuations. Such an analysis provides a basis for stochastic computational reliability analysis.

The mathematical formulation and computational implementation of the generalized perturbation‐based stochastic finite element method (SFEM) is the main contribution of the paper.

Many analysis and design problems in engineering and science involve uncertainty to varying degrees. This paper is concerned with the structural vibration problem involving uncertain material or geometric parameters, specified as fuzzy parameters. The requirement is to propagate the parameter uncertainty to the eigenvalues of the structure, specified as fuzzy eigenvalues. However, the usual approach is to transform the fuzzy problem into several interval eigenvalue problems by using the α-cuts method. Solving the interval problem as a generalized interval eigenvalue problem in interval mathematics will produce conservative bounds on the eigenvalues. The purpose of this paper is to investigate strategies to efficiently solve the fuzzy eigenvalue problem.

Based on the fundamental perturbation principle and vertex theory, an efficient perturbation method is proposed, that gives the exact extrema of the first-order deviation of the structural eigenvalue. The fuzzy eigenvalue approach has also been improved by reusing the interval analysis results from previous α-cuts.

The proposed method was demonstrated on a simple cantilever beam with a pinned support, and produced very accurate fuzzy eigenvalues. The approach was also demonstrated on the model of a highway bridge with a large number of degrees of freedom.

This proposed Vertex-Perturbation method is more efficient than the standard perturbation method, and more general than interval arithmetic methods requiring the non-negative decomposition of the mass and stiffness matrices. The new increment method produces highly accurate solutions, even when the membership function for the fuzzy eigenvalues is complex.

The purpose of this paper is to study the effect of J₃ perturbation of the Earth’s oblateness on satellite orbit compared with J₂ perturbation.

Based on the parametric variation method in the time domain, considering more accurate Earth potential function by considering J₃-perturbation effect, the perturbation equations about satellite’s six orbital elements (including semi-major axis, orbit inclination, right ascension of the ascending node, true anomaly, eccentricity and argument of perigee) has been deduced theoretically. The disturbance effects of J₂ and J₃ perturbations on the satellite orbit with different orbit inclinations have been studied numerically.

With the inclination increasing, the maximum of the semi-major axis increases weakly. The difference of inclination disturbed by the J₂ and J₃ perturbation is relative to orbit inclinations. J₃ perturbation has weak effect on the right ascension and argument of perigee. The critical angle of the right ascension and argument of perigee which decides the precession direction is 90° and 63.43°, respectively. The disturbance effects of J₂ and J₃ perturbations on the argument of perigee, right ascension and eccentricity are weakened when the eccentricity increases, simultaneously, the difference of J₂ and J₃ perturbations on argument of perigee, right ascension and argument of perigee decreases with eccentricity increasing, respectively.

In the future, satellites need to orbit the Earth much more precisely for a long period. The J₃ perturbation effect and the weight compared to J₂ perturbation in LEO can provide a theoretical reference for researchers who want to improve the control accuracy of satellite. On the other hand, the theoretical analysis and simulation results can help people to design the satellite orbit to avoid or diminish the disturbance effect of the Earth’s oblateness.

The J₃ perturbation equations of satellite orbit elements are deduced theoretically by using parametric variation method in this paper. Additionally, the comparison studies of J₂ perturbation and J₃ perturbation of the Earth’s oblateness on the satellite orbit with different initial conditions are presented.

Derives a first order perturbation algorithm for the computation of mean values and (co‐) variances of the transient temperature field in conduction heated materials with random field parameters. Considers both linear as well as non‐linear heat conduction problems. The algorithm is advantageous in terms of computer time compared to the Monte Carlo method. The computer time can further be reduced by appropriate transformation of the random vectors resulting from the discretization of the random fields.

The development of a numerical implementation of the small signal response of the MOS (Metal‐Oxide‐Silicon) capacitor using time perturbation analysis is discussed. The effects of nonconstant doping profiles and interface and bulk traps are included. The model uses Fermi‐Dirac statistics to describe the occupancy of the interface and bulk traps. The oxide region is considered to have no mobile carriers and any fixed oxide charge distribution is modeled as a charge sheet at the Si‐SiO2 interface. This technique can be used to find the small signal response of the device from the static solution.