title: Voices of the land: Richard Nunns in conversation with Martin Lodge

authors: Nunns, Richard

abstract: Richard Nunns in conversation with Martin Lodge

text: Voices of the land: Richard Nunns in conversation with Martin Lodge Richard Nunns in conversation with Martin Lodge

year: 2008

title: Maori syllabus and the curriculum documents: A critical analysis. Part 1: Tihe Mauri Ora

authors: Crombie, Winifred

subjects: Te reo Māori

abstract: This paper presents, within the context of ongoing debates on syllabus design, a critical analysis of Tihē Mauri Ora, a syllabus document produced by the New Zealand Ministry of Education to support the teaching and learning of the Māori language in schools in New Zealand. It includes a number of suggestions in relation to any future documents prepared with similar intent.

text: Maori syllabus and the curriculum documents: A critical analysis. Part 1: Tihe Mauri Ora This paper presents, within the context of ongoing debates on syllabus design, a critical analysis of Tihē Mauri Ora, a syllabus document produced by the New Zealand Ministry of Education to support the teaching and learning of the Māori language in schools in New Zealand. It includes a number of suggestions in relation to any future documents prepared with similar intent.

year: 2001

title: The use of positive and negative penalty functions in solving constrained optimization problems and partial differential equations

authors: Monterrubio Salazar, Luis Emilio

subjects: Rayleigh-Ritz Method

abstract: The Rayleigh-Ritz Method together with the Penalty Function Method is used to investigate the use of different types of penalty parameters. The use of artificial springs as penalty parameters is a very well established procedure to model constraints in the Rayleigh-Ritz Method, the Finite Element Method and other numerical methods. Historically, large positive values were used to define the stiffness coefficient of artificial springs, until recent publications demonstrated that it is possible to use negative values to define the stiffness coefficients of the springs. Furthermore, recent publications show that constraints can be enforced using positive and negative mass or inertia in vibration problems and in a more generic sense using eigenpenalty parameters which are penalty parameters in the matrix associated with the eigenvalue. Before the commencement of this thesis, solutions using artificial inertia were published only for beams and simple spring-mass systems.
In this thesis the use of all possible types of penalty parameters are investigated in vibration problems of Euler-Bernoulli beams, thin plates and shallow shells and in elastic stability analysis of Euler-Bernoulli beams, including penalty parameters associated with the geometrical stiffness matrix. The study includes the use of penalty parameters for both enforcing support boundary conditions and continuity conditions along structural joints.
This investigation started with the selection of the set of admissible functions that would: (a) allow modelling of beams, plates and shells in completely free boundary conditions; (b) not present any limitation in the number of functions that can be used in the solution. This gives the possibility to converge to the constraint solution and to model any type of boundary conditions.
The procedure proposed in this work combines several advantages: accuracy of the results, relative fast convergence, simplicity of the set of admissible functions and flexibility to define boundary conditions. While there are other procedures that may give better accuracy for specific cases, the proposed method is more widely applicable.
The procedure used in this work also includes a way to check for round-off errors and ill-conditioning in the results; as well as a way to bracket the  exact  solution with upper and lower-bound results.

text: The use of positive and negative penalty functions in solving constrained optimization problems and partial differential equations The Rayleigh-Ritz Method together with the Penalty Function Method is used to investigate the use of different types of penalty parameters. The use of artificial springs as penalty parameters is a very well established procedure to model constraints in the Rayleigh-Ritz Method, the Finite Element Method and other numerical methods. Historically, large positive values were used to define the stiffness coefficient of artificial springs, until recent publications demonstrated that it is possible to use negative values to define the stiffness coefficients of the springs. Furthermore, recent publications show that constraints can be enforced using positive and negative mass or inertia in vibration problems and in a more generic sense using eigenpenalty parameters which are penalty parameters in the matrix associated with the eigenvalue. Before the commencement of this thesis, solutions using artificial inertia were published only for beams and simple spring-mass systems.
In this thesis the use of all possible types of penalty parameters are investigated in vibration problems of Euler-Bernoulli beams, thin plates and shallow shells and in elastic stability analysis of Euler-Bernoulli beams, including penalty parameters associated with the geometrical stiffness matrix. The study includes the use of penalty parameters for both enforcing support boundary conditions and continuity conditions along structural joints.
This investigation started with the selection of the set of admissible functions that would: (a) allow modelling of beams, plates and shells in completely free boundary conditions; (b) not present any limitation in the number of functions that can be used in the solution. This gives the possibility to converge to the constraint solution and to model any type of boundary conditions.
The procedure proposed in this work combines several advantages: accuracy of the results, relative fast convergence, simplicity of the set of admissible functions and flexibility to define boundary conditions. While there are other procedures that may give better accuracy for specific cases, the proposed method is more widely applicable.
The procedure used in this work also includes a way to check for round-off errors and ill-conditioning in the results; as well as a way to bracket the  exact  solution with upper and lower-bound results.

year: 2009