Design sensitivity analysis for shape optimization based on the Lie derivative

peer reviewedAbstract The paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations. The proposed approach, based on geometrical concepts borrowed from differential geometry, shows that sensitivity of a performance function (i.e. any function of the solution of the problem) with respect to a given design variable can be represented mathematically as a Lie derivative, i.e. the derivative of that performance function along a flow representing the continuous shape modification of the geometrical model induced by the variation of the considered design variable. Theoretical formulae to express sensitivity analytically are demonstrated in detail in the paper, and applied to a nonlinear magnetostatic and a linear elastic problem, following both the direct and the adjoint approaches. Following the analytical approach, one linear system of which only the right-hand side needs be evaluated (the system matrix being known already) has to be solved for each of the design variables in the direct approach, or for each performance functions in the adjoint approach. A substantial gain in computation time is obtained this way compared to a finite difference evaluation of sensitivity, which requires solving a second nonlinear system for each design variable. This is the main motivation of the analytical approach. There is some freedom in the definition of the auxiliary flow that represents the shape modification. We present a method that makes benefit of this freedom to express sensitivity locally as a volume integral over a single layer of finite elements connected to both sides of the surfaces undergoing shape modification. All sensitivity calculations are checked with a finite difference in order to validate the analytic approach. Convergence is analyzed in 2D and 3D, with first and second order finite elements

THE DOMINATION OF THE GOVERNMENT IN THE POLITICAL SYSTEM OF THE REPUBLIC OF MACEDONIA

The 1991 Constitution of the Republic of Macedonia inaugurated the system of division of powers as a fundamental value of the constitutional order. It abandoned the system of unity government (the assembly system), along with the one-party system, and substituted them with the multiparty parliamentary system. According to the principle of the division of powers, the power is divided into legislative, executive, and judicial (Article 8, item 4 of the Constitution of the Republic of Macedonia). The legislative authority is exercised by the Assembly; the executive is shared between the Government and the President; and the judicial power is exercised by the courts. Nevertheless, parliamentary democracy is not determined only by the constitutional framework, but also by the (un) democratic tradition, the model of political culture, as well as the electoral and party system. In this sense, the same normative model works differently in different countries or at different periods of the development of the same political system. This is especially evident in the relations between parliament and government. The dominance of the executive is not only a characteristic of the model of organization of power in the Republic of Macedonia, but it is also a global tendency. In this sense, the parliament of the Republic of Macedonia shares the ‘fate’ of the representative bodies in contemporary parliamentarism. However, in the absence of a democratic tradition, the presence of subject political culture, the strong elements of partocracy and the party state, the fragile and fragmented civil society, and the weak general public, gives dramatic dimensions to the dominance of the executive over the legislative power

The Legal and Political Grounds for, and the Influence of the Actual Situation on, the Demand of the Albanians of Kosovo for Independence

The Article argues in support of the Kosovar Albanians\u27 right to independence and self-determination. By examining the ancient and recent ethnic history of these people and their neighbors, particularly the Serbs, the author brings to light the shared beliefs within each group. Then by examining developments since the dissolution of the Federal Republic of Yugoslavia, through the lenses of international law and politics, the author analyzes the building blocks of sovereign statehood: defined borders, governmental institutions, and international recognition

THE DOMINATION OF THE GOVERNMENT IN THE POLITICAL SYSTEM OF THE REPUBLIC OF MACEDONIA

The 1991 Constitution of the Republic of Macedonia inaugurated the system of division of powers as a fundamental value of the constitutional order. It abandoned the system of unity government (the assembly system), along with the one-party system, and substituted them with the multiparty parliamentary system. According to the principle of the division of powers, the power is divided into legislative, executive, and judicial (Article 8, item 4 of the Constitution of the Republic of Macedonia). The legislative authority is exercised by the Assembly; the executive is shared between the Government and the President; and the judicial power is exercised by the courts. Nevertheless, parliamentary democracy is not determined only by the constitutional framework, but also by the (un) democratic tradition, the model of political culture, as well as the electoral and party system. In this sense, the same normative model works differently in different countries or at different periods of the development of the same political system. This is especially evident in the relations between parliament and government. The dominance of the executive is not only a characteristic of the model of organization of power in the Republic of Macedonia, but it is also a global tendency. In this sense, the parliament of the Republic of Macedonia shares the ‘fate’ of the representative bodies in contemporary parliamentarism. However, in the absence of a democratic tradition, the presence of subject political culture, the strong elements of partocracy and the party state, the fragile and fragmented civil society, and the weak general public, gives dramatic dimensions to the dominance of the executive over the legislative power

Κυματίζοντας την αλβανικότητα. Κοινότοπος εθνικισμός στις ειδησεογραφικές ιστοσελίδες στην Αλβανία

Διατριβή (Διδακτορική)--Πανεπιστήμιο Μακεδονίας, Θεσσαλονίκη, 2022