Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness

Mathematical model to account for non-homogeneity of plate material is designed, keeping in mind all the physical aspects, and analyzed by applying quintic spline technique for the first time. This method has been applied earlier for other geometry of plates which shows its utility. Accuracy and versatility of the technique are established by comparing with the well-known existing results. Effect of quadratic thickness variation, an exponential variation of non-homogeneity in the radial direction, and variation in density; for the three different outer edge conditions namely clamped, simply supported and free have been computed using MATLAB for the first three modes of vibration. For all the three edge conditions, normalized transverse displacements for a specific plate have been presented which shows the shiftness of nodal radii with the effect of taperness.

Architecture's Tightrope - Investigating an Alternative Trajectory for Critical Architecture: Critical Spatial Practices and a Polycontextual Engagement with an Urban Thick Edge Condition

<p>This thesis investigation engages two contemporary interrelated problems – one theoretical and one practical – both of which are interrogated, interwoven and tested through a critical lens. The theoretical context framing the design-research reconsiders the vitality of ‘critical architecture’ in relation to contemporary discourse, in particular, the so-called ‘crisis of criticality’ and the implications of this ideological landscape within the built environment. Foregrounding a position to test this theoretical framing, the practical context of the design-research is distinctly urban – engaging one of the contemporary negative outcomes of rapid urbanisation. The practical problem investigates the ‘thick edges’ (places of singular and/or impermeable identities) that manifest around and below new urban motorway infrastructural developments, a condition that creates barriers to cultural, social and spatial flows between communities in urban settings. This thesis argues that by engaging with the complex and multiple cultural conditions of urban sites, the rigidity and singular nature of these impermeable thick edge spaces can be opened to diverse flows relating to multiple contexts. Through processes of design intervention, the thesis proposes a ‘polycontextual’ approach to introduce flows of wider contextual dimensions within an urban site – promoting architectural solutions that blur, fray and punctuate thick edges by developing them as threshold conditions between adjacencies. The theoretical problem analyses the limitations of both the autonomous and post-critical positions; this thesis argues that an alternative trajectory for a contemporary critical architecture has emerged, one that may be used as a theoretical framework for resolving urban thick edge conditions. Jane Rendell, Kim Dovey and Murray Fraser reveal a trajectory to shift architectural practices towards positive and flexible modes of production whilst simultaneously opposing the insufficient positions of the post-critical. They posit that architecture remains an inherently cultural proposition – created through constructive ‘relays’ that can mediate between theory and design – elucidating strategies of resistance through an engagement with practices that are both critical and spatial. Jane Rendell further argues that strategies for such ‘critical spatial practices’ can be elucidated through an examination of processes that are: site-specific, socio-spatial, and temporal. Adopting these three categories as the theoretical framework of this thesis focuses the design-research, implicating critical spatial practices as a contemporary and alternative position for critical architectural production - providing a framework for positive and critical positions in current discourse. In response to this two-fold investigation, the thesis tests a synthesis of critical spatial practices and a polycontextual approach through strategic designresearch propositions. Architecture’s Tightrope proposes a multifunctional events facility that permanently supports the New Zealand International Arts Festival, and the structuration of a dynamic, relational and non-deterministic public space. The primary aims of this thesis are: to test a contemporary critically engendered framework for architectural design-research that is both culturally and formally negotiated; and to investigate the potential for this framework to invert the negative conditions of urban thick edges through an engagement with multiple contexts.</p>

Architecture's Tightrope - Investigating an Alternative Trajectory for Critical Architecture: Critical Spatial Practices and a Polycontextual Engagement with an Urban Thick Edge Condition

<p>This thesis investigation engages two contemporary interrelated problems – one theoretical and one practical – both of which are interrogated, interwoven and tested through a critical lens. The theoretical context framing the design-research reconsiders the vitality of ‘critical architecture’ in relation to contemporary discourse, in particular, the so-called ‘crisis of criticality’ and the implications of this ideological landscape within the built environment. Foregrounding a position to test this theoretical framing, the practical context of the design-research is distinctly urban – engaging one of the contemporary negative outcomes of rapid urbanisation. The practical problem investigates the ‘thick edges’ (places of singular and/or impermeable identities) that manifest around and below new urban motorway infrastructural developments, a condition that creates barriers to cultural, social and spatial flows between communities in urban settings. This thesis argues that by engaging with the complex and multiple cultural conditions of urban sites, the rigidity and singular nature of these impermeable thick edge spaces can be opened to diverse flows relating to multiple contexts. Through processes of design intervention, the thesis proposes a ‘polycontextual’ approach to introduce flows of wider contextual dimensions within an urban site – promoting architectural solutions that blur, fray and punctuate thick edges by developing them as threshold conditions between adjacencies. The theoretical problem analyses the limitations of both the autonomous and post-critical positions; this thesis argues that an alternative trajectory for a contemporary critical architecture has emerged, one that may be used as a theoretical framework for resolving urban thick edge conditions. Jane Rendell, Kim Dovey and Murray Fraser reveal a trajectory to shift architectural practices towards positive and flexible modes of production whilst simultaneously opposing the insufficient positions of the post-critical. They posit that architecture remains an inherently cultural proposition – created through constructive ‘relays’ that can mediate between theory and design – elucidating strategies of resistance through an engagement with practices that are both critical and spatial. Jane Rendell further argues that strategies for such ‘critical spatial practices’ can be elucidated through an examination of processes that are: site-specific, socio-spatial, and temporal. Adopting these three categories as the theoretical framework of this thesis focuses the design-research, implicating critical spatial practices as a contemporary and alternative position for critical architectural production - providing a framework for positive and critical positions in current discourse. In response to this two-fold investigation, the thesis tests a synthesis of critical spatial practices and a polycontextual approach through strategic designresearch propositions. Architecture’s Tightrope proposes a multifunctional events facility that permanently supports the New Zealand International Arts Festival, and the structuration of a dynamic, relational and non-deterministic public space. The primary aims of this thesis are: to test a contemporary critically engendered framework for architectural design-research that is both culturally and formally negotiated; and to investigate the potential for this framework to invert the negative conditions of urban thick edges through an engagement with multiple contexts.</p>

Synergistically Exploiting CNN Pruning and HLS Versioning for Adaptive Inference on Multi-FPGAs at the Edge

FPGAs, because of their energy efficiency, reconfigurability, and easily tunable HLS designs, have been used to accelerate an increasing number of machine learning, especially CNN-based, applications. As a representative example, IoT Edge applications, which require low latency processing of resource-hungry CNNs, offload the inferences from resource-limited IoT end nodes to Edge servers featuring FPGAs. However, the ever-increasing number of end nodes pressures these FPGA-based servers with new performance and adaptability challenges. While some works have exploited CNN optimizations to alleviate inferences’ computation and memory burdens, others have exploited HLS to tune accelerators for statically defined optimization goals. However, these works have not tackled both CNN and HLS optimizations altogether; neither have they provided any adaptability at runtime, where the workload’s characteristics are unpredictable. In this context, we propose a hybrid two-step approach that, first, creates new optimization opportunities at design-time through the automatic training of CNN model variants (obtained via pruning) and the automatic generation of versions of convolutional accelerators (obtained during HLS synthesis); and, second, synergistically exploits these created CNN and HLS optimization opportunities to deliver a fully dynamic Multi-FPGA system that adapts its resources in a fully automatic or user-configurable manner. We implement this two-step approach as the AdaServ Framework and show, through a smart video surveillance Edge application as a case study, that it adapts to the always-changing Edge conditions: AdaServ processes at least 3.37× more inferences (using the automatic approach) and is at least 6.68× more energy-efficient (user-configurable approach) than original convolutional accelerators and CNN Models (VGG-16 and AlexNet). We also show that AdaServ achieves better results than solutions dynamically changing only the CNN model or HLS version, highlighting the importance of exploring both; and that it is always better than the best statically chosen CNN model and HLS version, showing the need for dynamic adaptability.

A Contribution to Analytical Solutions for Buckling Analysis of Axially Compressed Rectangular Stiffened Panels

Analytical solution to the buckling problems of stiffened panels subjected to in-plane compressive loads is presented. The total potential energy functional of stiffened panel is obtained by the summation of that of a line continuum and stiffened panel derived from elastic principles of mechanics. Minimizing the resulting equation with respect to deflection coefficient and rearranging gives the expression for obtaining the buckling load of stiffened panel. Exact deflection functions were substituted directly in the new solution and various edge conditions were considered in this analysis. Obtained results were compared with analytical results of previous works. The method is computationally efficient for complex edge conditions and gives high numerical accuracy.

Advancing a generalized method for solving problems of continuum mechanics as applied to the Cartesian coordinate system

Solving the problem of continuum mechanics has revealed the defining generalizations using the function argument method. The aim of this study was to devise new approaches to solving problems of continuum mechanics using defining generalizations in the Cartesian coordinate system. Additional functions, or the argument of the coordinates function of the deformation site, are introduced into consideration. The carriers of the proposed function arguments should be basic dependences that satisfy the boundary or edge conditions, as well as functions that simplify solving the problem in a general form. However, there are unresolved issues related to how not the solutions themselves should be determined but the conditions for their existence. Such generalized approaches make it possible to predict the result for new applied problems, expand the possibilities of solving them in order to meet a variety of boundary and edge conditions. The proposed approach makes it possible to define a series of function arguments, each of which can be a condition of uniqueness for a specific applied problem. Such generalizations concern determining not the specific functions but the conditions of their existence. From these positions, the flat problem was solved in the most detailed way, was tested, and compared with the studies reported by other authors. Based on the result obtained, a mathematical model of the flat applied problem of the theory of elasticity with complex boundary conditions was built. Expressions that are presented in coordinateless form are convenient for analysis while providing a computationally convenient context. The influence of the beam shape factor on the distribution of stresses in transition zones with different intensity of their attenuation has been shown. By bringing the solution to a particular result, the classical solutions have been obtained, which confirms its reliability. The mathematical substantiation of Saint-Venant's principle has been constructed in relation to the bending of a beam under variable asymmetric loading

Use of Higher Order Plate Theory in dynamic analysis of SSFS and CSFS thick rectangular plates in orthogonal polynomials

This study applied polynomial expressions as displacement and shear deformation functions in the free-vibration study of thick and moderately thick isotropic rectangular plates. Rectangular plates with two different edge conditions investigated in this work are: one with simple supports at three of its edges and with no support at the other edge denoted with the acronym (SSFS) and a rectangular plate with simple supports at opposite edges while the other opposite edges has a fixed support at one edge and no support at the other edge, this is denoted with the acronym (CSFS). The total potential energy of the plate was derived using the general theory of elasticity. The general governing equation of the plate was derived by minimizing the total potential energy equation of the plate. Edge conditions of the SSFS and CSFS plates were met and substituted into the general governing equation to obtain a linear expression which was solved to generate fundamental natural frequency function for the plates with various span-depth proportion (m/t) and planar dimensions proportion (n/m). The results obtained from this research were found to agree favourably with the results of similar problems in the literature upon comparison.

Accurate Results for Free Vibration of Doubly Curved Shallow Shells of Rectangular Planform (Part.1)

A method is presented for determining the free vibration frequencies of doubly curved, isotropic shallow shells under general edge conditions and is used to obtain accurate natural frequencies for wide range of geometric parameters. Based on the shallow shell theory applicable to thin thickness shells, a method of Ritz is extended to derive a frequency equation wherein the displacement functions are modified to accommodate arbitrary sets of edge conditions for both in-plane and out-of-plane motions. In numerical computation, convergence is tested against series terms and comparison study is made with existing results by other authors. Twenty one sets of frequency parameters are tabulated for a wide range of shell shape and curvature ratio to serve as data for future comparison and practical design purpose.

Calculation of the tense-deformed state of two ortogonal attended plates at the regional terms of symmetry through the matrices of Grina type

Purpose. Calculate the tense-deformed state of two ortogonal attended plates through special the built matrices of Grina type. Research methods. Bases of theory of laminas, apparatus of trigonometric rows of Fourier, methods: border-component tasks, variation of arbitrary permanent, matrices of Grina type. Results. A task of elastic elastic equilibrium of plate pairs connected at right angle was considered. On parallel edges of component body to connection rib special edge conditions – conditions of symmetry – were chosen. From the physical point of view the probed body can be the model of lateral walls of parallelepiped. It is provided the special terms of symmetry on both edges of component body, which are parallel to the rib of connection of plates. The method of calculation allows to calculate the tense-deformed state of spatial construction consisting of two plates in edge conditions of arbitrary surface loading. The results of calculation (as lines of level) of basic characteristics of static deformation of considered rectangular connection of two plates are given. Scientific novelty. The method of calculation of pair of plates, united at right angles was improved at the regional terms of symmetry, with subsequent graphic illustration of achived results. Practical value. The task probed in-process designs the phenomena which take place, at deformation of elements of vulcanization equipment. Achived results allow to find pequliarities of elements work of construction of complext structure and to promote its efficiency by optimization of component parameters parts.