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This study aims to propose a general and efficient adaptive strategy with local mesh refinement for two-dimensional (2D) finite element (FE) analysis based on the element energy projection (EEP) technique.

In view of the inflexibility of the existing global dimension-by-dimension (D-by-D) recovery method via EEP technique, in which displacements are recovered through element strips, an improved element D-by-D recovery strategy was proposed, which enables the EEP recovery of super-convergent displacements to be implemented mostly on a single element. Accordingly, a posteriori error estimate in maximum norm was established and an EEP-based adaptive FE strategy of h-version with local mesh refinement was developed.

Representative numerical examples, including stress concentration and singularity problems, were analyzed; the results of which show that the adaptively generated meshes reasonably reflect the local difficulties inherent in the physical problems and the proposed adaptive analysis can produce FE displacement solutions satisfying the user-specified tolerances in maximum norm with an almost optimal adaptive convergence rate.

The proposed element D-by-D recovery method is a more efficient and flexible displacement recovery method, which is implemented mostly on a single element. The EEP-based adaptive FE analysis can produce displacement solutions satisfying the specified tolerances in maximum norm with an almost optimal convergence rate and thus can be expected to apply to other 2D problems.

Policy is key for effective displacement governance in times of crises and in response and recovery. Therefore, this study assessed if Australian climate, disaster and emergency management policies provide effective mechanisms for governing displacement crises and areas where current approaches could be improved.

This study assessed 18 national and state-level disaster, emergency and climate change management frameworks to determine if best practice displacement governance themes were reflected in policy documents. Deductive thematic analysis was undertaken using Braun and Clarke’s six-phase method.

Issues of displacement are reflected in policies analysed in this study. However, current policy frameworks need to be equipped to comprehensively address the housing requirements of displaced people or provide long-term initiatives. Approaches are focused on crisis management rather than pre-emptively planning for displacement response and recovery. Therefore, Australia has not exercised national responsibility for displaced people appropriately.

Disaster displacement is an under-researched area of Australian scholarship and disaster management policy and practice. Therefore, this paper has practical implications in so far as it draws attention to the issue of displacement in Australia. A limitation of this paper is that it only analysed policy frameworks specific to disasters. While broader engagement was outside the scope of this study, this limitation provides opportunities for further research from disciplinary perspectives of public housing and homelessness to examine displacement policy challenges in these fields. Furthermore, this study is limited to a theoretical inquiry into this topic through a desktop review of policy documents. While this is a necessary first step, empirical studies are required to determine accurate displacement rates, drivers and people’s experience of being displaced.

This research aims to inform policy by presenting recommendations for policy interventions for disaster displacement governance. Therefore, this research has practical implications as policy and disaster risk reduction (DRR) professionals can draw from the findings of this research when planning and initiating disaster response for displaced persons.

This research draws attention to an area of disaster management practice and policy that has not been adequately accounted for. Highlighting gaps in current policy can assist in developing targeted strategies and solutions for internally displaced people, which protect their rights and meet their needs.

Displacement is a growing climate change issue. This research aims to help address this problem by drawing attention to areas where Australian disaster management approaches fail to account for displaced populations. Therefore, this research has practical implications for addressing future issues of disaster injustice that may arise if displacement continues, unacknowledged in disaster management.

Shape memory polymers (SMPs) are classified as smart materials owing to their inherent stimulus-induced response. SMPs are capable of recovering partially or totally to its original shape after a high degree of deformation by external stimulus. The most used stimuli are thermal, light, magnetic field and electricity. This research aims to characterize the toughness property of thermo-responsive SMP specimens fabricated by the material extrusion (ME) process and to investigate the impact of ME parameters on specimen maximum load and load-displacement curves. Moreover, to investigate the recovery efficiency based on the initial and post toughness generated by the compact tension test.

A design of experiments with three parameters (temperature, velocity and layer height) defined the ME settings to fabricate the specimens. The ME raster orientation factor was also evaluated separately. In addition, one more specimen group assisted by a clamp during the recovery process was compared with a specimen control group. After fabrication, specimens were submitted to a thermo-mechanical cycle that encompasses a compact tension test and a thermo-recovery process. Comparison studies of load-displacement, toughness and recovery efficiency of the specimens were carried out to determine the optimized fabrication parameters.

It was found that ME parameters and raster orientation impacted the test results. Samples with the clamp support during recovery returned a higher toughness than samples without support. Finally, results showed that the shape memory effect can contribute with up to 43 per cent recovery efficiency in a first recovery and up to 23 per cent in a second recovery of damaged specimens.

This paper is a reference for toughness and recovery properties of SMP parts produced by the ME fabrication process.

This study aims to provide a reliable and effective algorithm that is suitable for addressing the problems of continuous orders of frequencies and modes under different boundary conditions, circumferential wave numbers and thickness-to-length ratios of moderately thick circular cylindrical shells. The theory of free vibration of rotating cylindrical shells is of utmost importance in fields such as structural engineering, rock engineering and aerospace engineering. The finite element method is commonly used to study the theory of free vibration of rotating cylindrical shells. The proposed adaptive finite element method can achieve a considerably more reliable high-precision solution than the conventional finite element method.

On a given finite element mesh, the solutions of the frequency mode of the moderately thick circular cylindrical shell were obtained using the conventional finite element method. Subsequently, the superconvergent patch recovery displacement method and high-order shape function interpolation techniques were introduced to obtain the superconvergent solution of the mode (displacement), while the superconvergent solution of the frequency was obtained using the Rayleigh quotient computation. Finally, the superconvergent solution of the mode was used to estimate the errors of the finite element solutions in the energy norm, and the mesh was subdivided to generate a new mesh in accordance with the errors.

In this study, a high-precision and reliable superconvergent patch recovery solution for the vibration modes of variable geometrical rotating cylindrical shells was developed. Compared with conventional finite element method, under the challenging varying geometrical circumferential wave numbers, and thickness–length ratios, the optimised finite element meshes and high-precision solutions satisfying the preset error limits were obtained successfully to solve the frequency and mode of continuous orders of rotating cylindrical shells with multiple boundary conditions such as simple and fixed supports, demonstrating good solution efficiency. The existing problem on the difficulty of adapting a set of meshes to the changes in vibration modes of different orders is finally overcome by applying the adaptive optimisation.

The approach developed in this study can accurately obtain the superconvergent patch recovery solution of the vibration mode of rotating cylindrical shells. It can potentially be extended to fine numerical models and high-precision computations of vibration modes (displacement field) and solid stress (displacement derivative field) for general structural special value problems, which can be extensively applied in the field of engineering computations in the future. Furthermore, the proposed method has the potential for adaptive analyses of shell structures and three-dimensional structures with crack damage. Compared with conventional finite element methods, significant advantages can be achieved by solving the eigenvalues of structures with high precision and stability.

A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique.

By linearizing the free vibration problem of elastic membranes into a series of linear equivalent problems, reliable a posteriori point-wise error estimator is constructed via EEP super-convergent technique. Hierarchical local mesh refinement is incorporated to better deal with tough problems.

Several classical examples were analyzed, confirming the effectiveness of the EEP-based error estimation and overall adaptive procedure equipped with a local mesh refinement scheme. The computational results show that the adaptively-generated meshes reasonably catch the difficulties inherent in the problems and the procedure yields both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm.

By reasonable linearization, the linear-problem-based EEP technique is successfully transferred to two-dimensional eigenproblems with local mesh refinement incorporated to effectively and flexibly deal with singularity problems. The corresponding adaptive strategy can produce both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm and thus can be expected to apply to other types of eigenproblems.

This study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.

An hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.

Numerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.

The proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

This study aims to overcome the involved challenging issues and provide high-precision eigensolutions. General eigenproblems in the system of ordinary differential equations (ODEs) serve as mathematical models for vector Sturm-Liouville (SL) and free vibration problems. High-precision eigenvalue and eigenfunction solutions are crucial bases for the reliable dynamic analysis of structures. However, solutions that meet the error tolerances specified are difficult to obtain for issues such as coefficients of variable matrices, coincident and adjacent approximate eigenvalues, continuous orders of eigenpairs and varying boundary conditions.

This study presents an h-version adaptive finite element method based on the superconvergent patch recovery displacement method for eigenproblems in system of second-order ODEs. The high-order shape function interpolation technique is further introduced to acquire superconvergent solution of eigenfunction, and superconvergent solution of eigenvalue is obtained by computing the Rayleigh quotient. Superconvergent solution of eigenfunction is used to estimate the error of finite element solution in the energy norm. The mesh is then, subdivided to generate an improved mesh, based on the error.

Representative eigenproblems examples, containing typical vector SL and free vibration of beams problems involved the aforementioned challenging issues, are selected to evaluate the accuracy and reliability of the proposed method. Non-uniform refined meshes are established to suit eigenfunctions change, and numerical solutions satisfy the pre-specified error tolerance.

The proposed combination of methodologies described in the paper, leads to a powerful h-version mesh refinement algorithm for eigenproblems in system of second-order ODEs, that can be extended to other classes of applications in damage detection of multiple cracks in structures based on the high-precision eigensolutions.

This study aims to develop an adaptive finite element method for structural eigenproblems of cracked Euler–Bernoulli beams via the superconvergent patch recovery displacement technique. This research comprises the numerical algorithm and experimental results for free vibration problems (forward eigenproblems) and damage detection problems (inverse eigenproblems).

The weakened properties analogy is used to describe cracks in this model. The adaptive strategy proposed in this paper provides accurate, efficient and reliable eigensolutions of frequency and mode (i.e. eigenpairs as eigenvalue and eigenfunction) for Euler–Bernoulli beams with multiple cracks. Based on the frequency measurement method for damage detection, using the difference between the actual and computed frequencies of cracked beams, the inverse eigenproblems are solved iteratively for identifying the residuals of locations and sizes of the cracks by the Newton–Raphson iteration technique. In the crack detection, the estimated residuals are added to obtain reliable results, which is an iteration process that will be expedited by more accurate frequency solutions based on the proposed method for free vibration problems.

Numerical results are presented for free vibration problems and damage detection problems of representative non-uniform and geometrically stepped Euler–Bernoulli beams with multiple cracks to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method.

The proposed combination of methodologies described in the paper leads to a very powerful approach for free vibration and damage detection of beams with cracks, introducing the mesh refinement, that can be extended to deal with the damage detection of frame structures.

Moderately thick circular cylindrical shells are widely used as supporting structures or storage cavities in structural engineering, rock engineering, and aerospace engineering. In practical engineering, shells often work with micro-cracks or defects. The existence of micro-crack damage may result in the disturbance of dynamic behaviours and even induce accidental dynamic disasters. The free vibration frequency and mode are important parameters for the dynamic performance and damage identification analysis. In particular, stiffness weakening of the local damage region leads to significant changes in the vibration mode, which makes it difficult for the mesh generated in the conventional finite element method to capture a high-precision solution of the local oscillation.

In response to the above problems, this study developed an adaptive finite element method and a crack damage characterisation method for moderately thick circular cylindrical shells. By introducing the inverse power iteration method, error estimation, and mesh subdivision refinement technique for the analysis of finite element eigenvalue problems, an adaptive computation scheme was constructed for the free vibration problem of moderately thick circular cylindrical shells with circumferential crack damage.

Based on typical numerical examples, the established adaptive finite element solution for the free vibration of moderately thick circular cylindrical shells demonstrated its suitability for solving the high-precision free vibration frequency and mode of cylindrical shell structures. The any order frequency and mode shape of cracked cylindrical shells under the conditions of different ring wave numbers, crack locations, crack depths, and multiple cracks were successfully solved. The influences of the location, depth, and number of cracks on the disturbance of dynamic behaviours were analysed.

This study can be used as a reference for the adaptive finite element solution of free vibration of moderately thick circular cylindrical shells with cracks and lays the foundation for further development of a high-performance computation method suitable for the dynamic disturbance and damage identification analysis of general cracked structures.

The study aims to analyze the roles of poverty and African American status in terms of vulnerability to tornado damages and barriers to recovery afterward.

Using five decades of county-level data on tornadoes, the authors test whether economic damages from tornadoes are correlated with vulnerability (proxied by poverty and African American status) and wealth (proxied by median income and educational attainment), controlling for tornado risk. A multinomial logistic difference-in-difference (DID) estimator is used to analyze long-run effects of tornadoes in terms of displacement (reduced proportions of the poor and African Americans), abandonment (increased proportions of those groups) and neither or both.

Controlling for tornado risk, poverty and African American status are linked to greater tornado damages, as is wealth. Absent tornadoes, displacement and abandonment are both more likely to occur in urban settings and communities with high levels of vulnerability, while abandonment is more likely to occur in wealthy communities, consistent with on-going forces of segregation. Tornado damages significantly increase abandonment in vulnerable communities, thereby increasing the prevalence of poor African Americans in those communities. Therefore, the authors conclude that tornadoes contribute to on-going processes generating inequality by poverty/race.

The current paper is the first study connecting tornado damages to race and poverty. It is also the first study finding that tornadoes contribute to long-term processes of segregation and inequality.