This paper is a survey of structural shape optimization with an emphasis on techniques dealing with shape optimization of the boundaries of two- and three-dimensional bodies. Attention is focused on the special problems of structural shape optimization which are due to a finite element model which must change during the optimization process. These problems include the requirement for sophisticated automated mesh generation techniques and careful choice of design variables. They also include special problems in obtaining sufficiently accurate sensitivity derivatives.

Structural shape optimization — a survey

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=1936&context=lkcsb_research

The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution

Behaviour of axially crushed corrugated tubes

Flexural free vibrations of rectangular plates with complex support conditions

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=1926&context=lkcsb_research

Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates

Fundamental Frequencies of Simply Supported but Partially Clamped Square Plates

Buckling problems of a rhomboidal plate with all edges clamped, on which compressive or shearing force is applied along its edges, are studied in this paper by using the energy method (Lagrangian multiplier method). Natural vibrations of the plate are also considered. The lowest buckling loads and the fundamental frequencies for several oblique angles are calculated. Convergency of the solutions is considered good enough.

Compressive or Shearing Buckling Load and Fundamental Frequency of a Rhomboidal Plate with All Edges Clamped

Effects of the contact condition at the first ridge on mechanical behaviors of threaded portions were analysed using an axi-symmetric FEM which is appropriate for the three-body elastic contact problem including the effects of friction on two contact surfaces between threads of bolt and nut, and between fastened plate and nut. The cross sectional shape of nut at the first ridge changes circumferentially due to the lead angle of thread, which causes non-symmetric mechanical behaviors concerning the ratio of flank loads and the stress concentration at the root of bolt. Four types of models were used to estimate these non-symmetric behaviors approximately. Each of them represents the cross section rotated one fourth revolution around axis. The analytical members are bolt, nut and fastened plate, and only the shape of nut is changed. The analysis is done by the axi-symmetric FEM without considering the effects of lead angle. The ratio of flank loads and the stress concentration at each cross section show some remarkable effects of the non-symmetric behaviors.

Stresses in Bolt and Nut : Effects of Contact Conditions at the First Ridge

Mechanical behaviors of a hollow-bolt are analysed by a finite element method (FEM) which can deal with the contact conditions of threaded portions correctly. The characteristics of the load of No.1 thread, which is the nearest one to the bearing surface of a nut, and the stress concentration at the root of No.1 thread of a bolt are discussed by varying the inside diameter of a hollow-bolt, the friction coefficient at pressure flank and the nominal diameter. The results obtained indicate that the values of the load of No.1 thread and the stress concentration factor show opposite features to the variations of the inside diameter and the nominal diameter. Therefore, the evaluations of strength of a hollow-bolt based on the load distribution are not always correct.

Ratio of Flank Loads of Screw Threads in Hollow-bolt

The problem of natural vibrations of an isosceles-triangular plate with all edges clamped or with two equal edges clamped and the base edge supported is treated in this paper by means of the energy method, which was applied by one of the authors to the eigenvalue problems of a rhomboidal plate with all edges clamped. Numerical values of the fundamental frequencies are calculated for plates with several contained angles, and they are checked by experiments.

Minoru Hamada

Papers

Fundamental Frequencies of Simply Supported but Partially Clamped Square Plates

Compressive or Shearing Buckling Load and Fundamental Frequency of a Rhomboidal Plate with All Edges Clamped

Stresses in Bolt and Nut : Effects of Contact Conditions at the First Ridge

Ratio of Flank Loads of Screw Threads in Hollow-bolt

Fundamental Frequency of an Isosceles-triangular Plate