scholarly journals Adjoint-based methods to compute higher-order topological derivatives with an application to elasticity

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Phillip Baumann ◽  
Kevin Sturm
Keyword(s):  
Linear Elasticity ◽  
Problem Formulation ◽  
Short Review ◽  
Higher Order ◽  
Second Order ◽  
Adjoint Variable ◽  
Content Type ◽  
Lagrangian Framework ◽  
Topological Derivatives ◽  
Derivatives Of

PurposeThe goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) constrained shape functionals.Design/methodology/approachThe authors employ the adjoint and averaged adjoint variable within the Lagrangian framework and compare three different adjoint-based methods to compute higher-order topological derivatives. To illustrate the methodology proposed in this paper, the authors then apply the methods to a linear elasticity model.FindingsThe authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutz' method, the averaged adjoint method and Delfour's method.Originality/valueIn contrast to other contributions regarding this subject, the authors not only compute the first- and second-order topological derivatives, but additionally give some insight on various methods and compare their applicability and efficiency with respect to the underlying problem formulation.

scholarly journals Sensitivity of the Second Order Homogenized Elasticity Tensor to Topological Microstructural Changes

2021 ◽  
Author(s):  
V. Calisti ◽  
A. Lebée ◽  
A. A. Novotny ◽  
J. Sokolowski
Keyword(s):  
Circular Inclusion ◽  
Elasticity Tensor ◽  
Second Order ◽  
Topological Derivative ◽  
Microstructural Changes ◽  
Topological Derivatives ◽  
Spatial Dimensions ◽  
Elasticity Tensors ◽  
Derivatives Of ◽  
Optimization Of Microstructures

AbstractThe multiscale elasticity model of solids with singular geometrical perturbations of microstructure is considered for the purposes, e.g., of optimum design. The homogenized linear elasticity tensors of first and second orders are considered in the framework of periodic Sobolev spaces. In particular, the sensitivity analysis of second order homogenized elasticity tensor to topological microstructural changes is performed. The derivation of the proposed sensitivities relies on the concept of topological derivative applied within a multiscale constitutive model. The microstructure is topologically perturbed by the nucleation of a small circular inclusion that allows for deriving the sensitivity in its closed form with the help of appropriate adjoint states. The resulting topological derivative is given by a sixth order tensor field over the microstructural domain, which measures how the second order homogenized elasticity tensor changes when a small circular inclusion is introduced at the microscopic level. As a result, the topological derivatives of functionals for multiscale models can be obtained and used in numerical methods of shape and topology optimization of microstructures, including synthesis and optimal design of metamaterials by taking into account the second order mechanical effects. The analysis is performed in two spatial dimensions however the results are valid in three spatial dimensions as well.

Linking transformational leadership and “multi-dimensions” of project success

2019 ◽  
Vol 13 (1) ◽  
pp. 103-127 ◽  
Author(s):  
Umer Zaman ◽  
Shahid Nawaz ◽  
Sidra Tariq ◽  
Asad Afzal Humayoun
Keyword(s):  
Transformational Leadership ◽  
Structural Equation ◽  
Structural Model ◽  
Project Success ◽  
Higher Order ◽  
Project Managers ◽  
Second Order ◽  
Equation Modeling ◽  
Content Type ◽  
The Relationship

Purpose Transformational leadership, flexibility and visibility improves project responsiveness to highly unpredictable and impactful events referred as the ‘black swans’ in mega projects (Bloch et al., 2012; Raziq et al., 2018; Zailani et al., 2016). However, these concepts have never been empirically tested in a single framework to determine their significant impact on multi-dimensional project success. The purpose of this paper is to investigate the interactional effects of project flexibility and project visibility on the relationship between transformational leadership and “multi-dimensions” of project success including meeting design goals; impact on customers and benefits to project-based organization. Design/methodology/approach Empirical data derived from cross-sectional survey of 160 project managers from telecom intensive companies in Pakistan were used to test the conceptual framework developed from recent literature. Partial least squares-structural equation modeling (PLS-SEM) provided detailed analysis of the measurement and structural model. The most recent reflective–formative PLS-SEM approach for higher-order constructs has been introduced. Findings The results indicate that project managers’ transformational leadership (β = 0.348, p < 0.01), project flexibility (β = 0.221, p < 0.01) and project visibility (β = 0.366, p < 0.01) are positively related with the multi-dimensional project success (second-order formative) construct. Interestingly, the relationship between transformational leadership and project success is influenced by significantly negative moderations established through project flexibility (β = −0.100, p < 0.01) and project visibility (β = −0.093, p < 0.05). Research limitations/implications This study in the telecom sector examined the interactional effects of risk mitigating strategies (i.e. project flexibility and project visibility) on the relationship between transformational leadership and multi-dimensional project success. This study creates a basis for future investigations extending to various project types and relevant to different industries especially those involving higher-order (formative) assessments of project success. Practical implications The study findings assist project leaders to meet their escalating commitments in achieving project success from a multi-dimensional standpoint. Additionally, this study underscores a renewed perspective of transformational leadership and project outcomes. Despite prevailing understanding developed through prior research, transformational leadership may become less favorable for project success in conditions of increased flexibility and visibility in projects. Originality/value Earlier studies have overlooked the multi-dimensional nature of project success (second-order formative) construct, despite several attempts to examine the interplay between transformational leadership and project success. Based on the knowledge gap and non-existence of empirical evidence, the authors introduced and empirically tested the moderating role of project flexibility and project visibility in the relationship between transformational leadership and multi-dimensional project success.

Development and validation of behavioral biases scale: a SEM approach

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ritika ◽  
Nawal Kishor
Keyword(s):  
Decision Making ◽  
Investment Decision ◽  
Phase 1 ◽  
Secondary Data ◽  
Higher Order ◽  
Second Order ◽  
Individual Investors ◽  
Content Type ◽  
Behavioral Biases ◽  
Investment Decision Making

PurposeThis paper attempts to identify the biases in decision-making of individual investors. The paper aims to develop and validate a higher-order behavioral biases scale.Design/methodology/approachScale development is done by identifying the relevant items of the scale through existing literature and then, adding new items for some biases. In phase 1, using a structured questionnaire, data was collected from 274 investors who invest in financial markets. The major dimensions of the scale have been pruned by using exploratory factor analysis administered on data collected in phase 1. Higher-order CFA is used to analyze the data and to validate the scale on another set of data (collected in phase 2) containing 576 investors.FindingsThe study reveals that the scale for measuring behavioral biases has many dimensions. It has two second-order factors and 13 zero-order constructs. Two second-order constructs have been modeled on the basis of cause of errors in investment decision-making, that is, biases caused due to cognition, biases caused due to emotions.Originality/valueBehavioral biases are yet to receive a due attention, especially, in the Indian context. The present research is focusing on providing an empirically tested scale to test the behavioral biases. Some of the biases, which have been analyzed using secondary data in previous studies, have been tested with the help of statements in this study.

Imaging of small penetrable obstacles based on the topological derivative method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lucas Fernandez ◽  
Ravi Prakash
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Second Order ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Content Type ◽  
Topology Optimization Problem ◽  
Order Reconstruction ◽  
Topological Derivatives

PurposeThe purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.Design/methodology/approachThe method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.FindingsIn this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.Originality/valueThe current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.

scholarly journals Affine differential geometry of osculating hypersurfaces

2012 ◽  
Vol 53 ◽  
pp. 37-41
Author(s):  
Kazimieras Navickis
Keyword(s):  
Differential Geometry ◽  
Higher Order ◽  
Second Order ◽  
Affine Differential Geometry ◽  
Local Properties ◽  
Derivatives Of

Osculating surfaces of second order have been studied in classical affine differential geometry [1].  In this article we generalize this notion to osculating hypersurfaces of higher order of hypersurfaces in Euclidean n-space. Various geometric interpretations are given. This yields a affinely invariant consideration of the local properties of a given hypersurface which depend on the derivatives of higher order.

Second-Order Design Sensitivity Analysis of Mechanical System Dynamics by a Mixed Direct Differentiation Adjoint Variable Method

1998 ◽  
Author(s):  
Javier Urruzola ◽  
José Manuel Jiménez
Keyword(s):  
Sensitivity Analysis ◽  
Design Sensitivity ◽  
Second Order ◽  
Variable Method ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Direct Differentiation ◽  
Design Variables ◽  
Adjoint Variables ◽  
Derivatives Of

Abstract This paper presents a new approach to second order sensitivity analysis of multibody dynamics. Adjoint variables together with direct differentiation are used to derive first- and second-order derivatives of measures of dynamic response with respect to design variables. It is shown that the proposed method can be compared advantageously to the fully adjoint variable method proposed by Haug in terms of simplicity and numerical cost. In order to validate the algorithm, a simple oscillator example proposed by Haug is solved analytically and by the mixed method, with identical results.

scholarly journals Osculating hypersurfaces of higher order

2011 ◽  
Vol 52 ◽  
Author(s):  
Kazimieras Navickis
Keyword(s):  
Differential Geometry ◽  
Higher Order ◽  
Second Order ◽  
Classical Differential Geometry ◽  
Derivatives Of

Oscurating surfaces of second order have been studied in classical differential geometry [1]. In this article we generalize this notion to osculating hyper-surfaces of higher order of hyper-surfaces inEuclidean n-space. Various related results are obtained using the derivatives of higher order.   

scholarly journals Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Lithium Niobate

2006 ◽  
Vol 3 (3) ◽  
pp. 122-133 ◽  
Author(s):  
Thresiamma Philip ◽  
C. S. Menon ◽  
K. Indulekha
Keyword(s):  
Energy Density ◽  
Lithium Niobate ◽  
Elastic Constants ◽  
Elastic Stiffness ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Gruneisen Parameters ◽  
Derivatives Of

The second and third-order elastic constants and pressure derivatives of second- order elastic constants of trigonal LiNbO3(lithium niobate) have been obtained using the deformation theory. The strain energy density estimated using finite strain elasticity is compared with the strain dependent lattice energy density obtained from the elastic continuum model approximation. The second-order elastic constants and the non-vanishing third-order elastic constants along with the pressure derivatives of trigonal LiNbO3are obtained in the present work. The second and third-order elastic constants are compared with available experimental values. The second-order elastic constant C11which corresponds to the elastic stiffness along the basal plane of the crystal is less than C33which corresponds to the elastic stiffness tensor component along thec-axis of the crystal. The pressure derivatives, dC'ij/dp obtained in the present work, indicate that trigonal LiNbO3is compressible. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in LiNbO3. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

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