The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensive...The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra（CGA）. The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.展开更多
In order to study the dynamic behaviour of construction,specifically seismic response of structures,as many researchers did,we have resorted to modelling methods,based on the scaled internal forces.Therefore,this rese...In order to study the dynamic behaviour of construction,specifically seismic response of structures,as many researchers did,we have resorted to modelling methods,based on the scaled internal forces.Therefore,this research includes results of an experimental investigation aimed to establish the possibility of realistic simulations of the cyclic response of small-scale models of one bay,one-storey reinforced concrete frames with masonry infills as a preliminary step for simulating the dynamic response of such structural.So,the specimens constructed were 1:9 scale R/C frames.These 1:9 scale infill frames were constructed with prototype materials and were tested in an extensive experimental sequence representing specimens of a scale near the prototype(1:3).The tested laboratory models include 1:3 scale infilled R/C frames that were built from original material such as steel,concrete and masonry infills(hollow masonry units and mortar).With the same scale,geometry and construction materials used for the construction of a 1:3 scale 5-story three dimensional building.This program consisted of 16 models,5 bare and 11 masonry infilled.all models refer to single-storey one-bay 1:9 scale as for the original structure and a one third of the scale(1:3)as for the prototype(1:3).The reinforced concrete specimens were designed in such a way as to prevent shear failure of the columns.Finally,the present paper was carried out in the Laboratory of Strength of Materials and Structures in the Department of Civil Engineering at Aristotle University of Thessaloniki.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.51375059)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA040203)+1 种基金Special Fund for Agro-scientific Research in the Public Interest of China(Grant No.201313009-06)National Key Technology R&D Program of the Ministry of Science and Technology of China(Grant No.2013BAD17B06)
文摘The solution for the forward displacement analysis（FDA） of the general 6-6 Stewart mechanism（i.e., the connection points of the moving and fixed platforms are not restricted to lying in a plane） has been extensively studied, but the efficiency of the solution remains to be effectively addressed. To this end, an algebraic elimination method is proposed for the FDA of the general 6-6 Stewart mechanism. The kinematic constraint equations are built using conformal geometric algebra（CGA）. The kinematic constraint equations are transformed by a substitution of variables into seven equations with seven unknown variables. According to the characteristic of anti-symmetric matrices, the aforementioned seven equations can be further transformed into seven equations with four unknown variables by a substitution of variables using the Grobner basis. Its elimination weight is increased through changing the degree of one variable, and sixteen equations with four unknown variables can be obtained using the Grobner basis. A 40th-degree univariate polynomial equation is derived by constructing a relatively small-sized 9 × 9 Sylvester resultant matrix. Finally, two numerical examples are employed to verify the proposed method. The results indicate that the proposed method can effectively improve the efficiency of solution and reduce the computational burden because of the small-sized resultant matrix.
文摘In order to study the dynamic behaviour of construction,specifically seismic response of structures,as many researchers did,we have resorted to modelling methods,based on the scaled internal forces.Therefore,this research includes results of an experimental investigation aimed to establish the possibility of realistic simulations of the cyclic response of small-scale models of one bay,one-storey reinforced concrete frames with masonry infills as a preliminary step for simulating the dynamic response of such structural.So,the specimens constructed were 1:9 scale R/C frames.These 1:9 scale infill frames were constructed with prototype materials and were tested in an extensive experimental sequence representing specimens of a scale near the prototype(1:3).The tested laboratory models include 1:3 scale infilled R/C frames that were built from original material such as steel,concrete and masonry infills(hollow masonry units and mortar).With the same scale,geometry and construction materials used for the construction of a 1:3 scale 5-story three dimensional building.This program consisted of 16 models,5 bare and 11 masonry infilled.all models refer to single-storey one-bay 1:9 scale as for the original structure and a one third of the scale(1:3)as for the prototype(1:3).The reinforced concrete specimens were designed in such a way as to prevent shear failure of the columns.Finally,the present paper was carried out in the Laboratory of Strength of Materials and Structures in the Department of Civil Engineering at Aristotle University of Thessaloniki.
