2101 A Method for Determining the Optimal Direction of the Principal Moment of Inertia in Frame Element Cross-Sections Based on the Complementary Energy and Its Application to Topology Optimization

2005 ◽  
Vol 2005.15 (0) ◽  
pp. 245-248
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Moment Of Inertia ◽  
Principal Moment ◽  
Complementary Energy ◽  
Frame Element ◽  
Optimal Direction

A Method for Determining the Optimal Direction of the Principal Moment of Inertia in Frame Element Cross-Sections

2004 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Moment Of Inertia ◽  
Structural Topology ◽  
Principal Moment ◽  
Frame Element ◽  
Optimal Direction ◽  
Conceptual Design Phase

This paper discusses a method to determine the optimal direction of the principal moment of inertia in frames element cross-sections for the design of mechanical structures at the conceptual design phase. The direction in each frame element is determined by maximizing the structural stiffness. Construction of the optimization procedure is based on the KKT-conditions and the balance of bending moments applied to each frame element. This method is implemented as an application in a structural topology optimization procedure that uses frame elements. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

2005 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Strain Energy ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Structural Topology ◽  
Energy Concept ◽  
Conceptual Design Phase ◽  
Complementary Strain ◽  
Topology Optimization Method

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

A Comparative Study of the Formulations for Topology Optimization of Compliant Mechanisms

2008 ◽  
Author(s):  
Sangamesh R. Deepak ◽  
M. Dinesh ◽  
Deepak Sahu ◽  
Salil Jalan ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Compliant Mechanisms ◽  
Computation Time ◽  
Initial Guess ◽  
Benchmark Problems ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Frame Element ◽  
Force Direction

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the last 15 years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parameterizations, namely, the frame element based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, the ability to converge from an unbiased uniform initial guess, and the computation time are analyzed. Some observations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

scholarly journals NUMERICAL INVESTIGATION OF THE ELASTIC-PLASTIC LINEAR HARDENING STRESS-STRAIN STATE OF THE FRAME ELEMENT CROSS-SECTION

2016 ◽  
Vol 8 (3) ◽  
pp. 94-100
Author(s):  
Andrius Grigusevičius ◽  
Gediminas Blaževičius
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Software Environment ◽  
Stress Strain ◽  
Hardening Material ◽  
Frame Element ◽  
Nonlinear Stress

The aim of this paper is to present a solution algorithm for determining the frame element crosssection carrying capacity, defined by combined effect of bending moment and axial force. The distributions of stresses and strains inside a cross-section made of linearly hardening material are analysed. General nonlinear stress-strain dependencies are composed. All relations are formed for rectangular cross-section for all possible cases of combinations of axial force and bending moment. To this end, five different stress-strain states are investigated and four limit axial force values are defined in the present research. The nonlinear problem is solved in MATLAB mathematical software environment. Stress-strain states in the cross-sections are investigated in detail and graphically analysed for two numerical experiments.

A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
M. Dinesh ◽  
Deepak K. Sahu ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Compliant Mechanisms ◽  
Initial Guess ◽  
Benchmark Problems ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Frame Element ◽  
Force Direction ◽  
Computer Codes

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the past 15years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parametrizations, namely, the frame element-based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, and the ability to converge from an unbiased uniform initial guess are analyzed. Some observations and recommendations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

scholarly journals IV. On the practical solution of the most general problems in continuous beams

1879 ◽  
Vol 29 (196-199) ◽  
pp. 493-505
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
General Problem ◽  
Bending Moment ◽  
Moment Of Inertia ◽  
Shearing Stress ◽  
Practical Solution ◽  
Continuous Beams ◽  
The Moment

1. It is not necessary to enter into the question of the advisability of employing continuous girders in bridges with spans of less than 200 feet, but it is generally conceded that the increased economy due to the employment of continuous girders in longer spans more than counterbalances the well-known practical objections to continuity. Hence the practical solution of the general problem—given the conditions at the ends of a continuous girder, the spans, the moment of inertia of all cross sections, and the loading, to find the bending moment and shearing stress in every cross-section, is not unworthy of our attention.

scholarly journals AUTO GENERATION OF THE CENTER OF GRAVITY OF TUBULAR STRUCTURES DURING CRUSH DEFORMATION

2009 ◽  
Vol 06 (02) ◽  
pp. 333-348 ◽  
Author(s):  
REZA AFSHAR ◽  
AIDY ALI ◽  
B. B. SAHARI
Keyword(s):  
Wall Thickness ◽  
Cross Sections ◽  
Center Of Gravity ◽  
Moment Of Inertia ◽  
Tubular Structures ◽  
Program Code ◽  
Axial Crush ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Axis I

Displacement of the center of gravity (COG) of tubular structures with various polygonal cross-sections is numerically investigated under an axial crush using the program code of ANSYS/LS-DYNA. A subroutine is developed using this code to calculate the COG of the deformed shape, during and after the crush. The effect of wall thickness on displacement of the COG is also investigated. Displacement of the COG decreases as the number of edges increases; it is a reasonable symmetric-deformed shape for the number of edges beyond eight. An even number of edges leads to a more symmetric displacement of the COG. The effect of the number of polygonal edges on symmetric deformation of the COG becomes more prominent as the initial wall thickness decreases. The higher number of edges stabilizes the deformed shape and the value of the mass moment of inertia of the deformed shape about the y axis (Iyy). The value of the mass moment of inertia about the x–z axes (Ixz) in comparison with Iyy can be neglected in the case of dealing with an axial crush along the y direction.

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