| The solid wood mortise-and-tenon(M&T)joint furniture is popular with consumers for its workmanlike structures,natural materials and various appearances.Structure design plays a vitally important role in development of furniture products,which influences the production processes,volume of materials and structure safety directly.However,the method of structure design is still depended on the experience of designer and limited measurements.In addition,furniture is regarded as two-dimensional structure and the joint was seen as rigid,when analyzed by mechanical analysis and finite element method(FEM).The final aim of this study is to shorten the cycle of furniture structure design,save materials and reduce the costs of furniture industrials.In this study,the M&T joint was regarded as semi-rigid joint,the mechanical properties of wood and joint were systematically studied,and then the finite element model of joint was build and applied to optimize the furniture structure.The specific works and results are shown as followings:1)In order to obtain the mechanical parameters used in finite elment model,the mechanical properties of beech(Fragus liskey)wood in elastoplastic stage were measured including elastic constants,yield and fracture strengths,as well as constitutive relation of true stress and strain of beech under compressive and tensile states.The finite element model of compressive and tensile were built based on the elastoplastic mechanical properties of beech and verified by experiments.The results of FEM were well consistent with those of experiments.Under compressive state,the errors in longitudinal,radial,and tangential directions were 13.69%,4.25%,and 4.81%respectively,and those in tensile state were 8.25%,4.27%,and 10.92%.It indicated that the FEM was able to be applied to predict the elastoplastic mechanical behaviors of beech.2)The anatomizing method of M&T joint was put forward,and the self-designed device used to measure the friction coefficient(FC)was designed.The influences of grain orientations,area,and contact force on FC were studied.In addition,the mechanical models and finite element models were established to predict the withdrawal and bending resistance.The experimental results showed that withdrawal resistances were 974.02(12.21)and 1609.46(12.45)N when the interferences are 0.1 and 0.2 mm respectively,and those of mechanical model were 1249.59 and2142.15 N with errors of 28.29%and 33.10%,besides,those of FEM were 7.78%and 21.73%respectively.In addition,the experimental results of bending resistances were 1138.13(6.83),1188.00(11.48),and 1229.07(6.10)N with tenon fits of 0,0.1,and 0.2 mm respectively.The results of mechanical model ranged from 1011 and 1348 N,and the errors between experiment and FEM were 2.51%,4.09%,and 4.54%respectively.Thus,the finite element model of joint was capable of predicting the withdrawal and bending resistances of T-shaped M&T joint.3)The mechanical properties of glued M&T joint were studied by anatomizing method,and its finite element model was built.The normal tensile strength,shear strengths,distributions of glue,and thickness of glue line in M&T joint were measured.In addition,the finite element model was built considering the physical and mechanical properties of joint based on the cohesive model and maximum stress law,and the validity of finite element model was verified by withdrawal and bending resistance tests.The results showed that experimental results of withdrawal resistances were 3155.48(1.6),4434.30(5.8),and 5133.01(4.3)N,when tenon fits were 0,0.1,and 0.2 mm respectively,and the errors between experiments and FEM were 2.36%,6.89%,and 1.56%respectively.The results of bending resistances were 1268.50(9.2),1151.63(1.5),and 1147.13(7.1)N with tenon fits of 0,0.1,and 0.2 mm respectively,and the errors between FEM and experiments were 11.22%,0.46%,and 1.95%respectively.4)The applicability of finite element model of M&T joint in structure design of furniture was studied and verified by using M&T joint stools.Firstly,the qualitative analysis of stress and strain distributions of stool was conducted.Secondly,the quantitative analysis of loading capacity of stool was investigated.The results showed that stress distributions of finite element model were in consistence with strain distributions of experiment.In addition,the loading capacities of nine stools predicted by FEM were consistent with those of experiments with errors within 21.44%.Summarizing the qualitative and quantitative analysis,the results of FEM and experiment were in good consistence.Thus,it was proved that the finite element model of M&T joint can be applied to structure design of solid wood M&T joint furniture.5)Taking the stool used above as an example,the optimal design method of solid wood M&T joint furniture was investigated.Firstly,the effect of stretchers'positions on the loading capacity of stool was studied by FEM,and then the relation between loading capacity and stretchers'positions was fitted by response surface method with R~2 of 0.88,which means the above method worked well.Secondly,the volume of stool was optimized by FEM and nonlinear optimization method of MATLAB.The results showed the optimized volume of stool was decreased by 43.35%.Thus,the method described above works well in structure and reduction design of solid wood M&T joint furniture.In conclusion,the anatomizing method can be used to study the mechanical properties of M&T joint.The finite element model built based on semi-rigid mechanical properties of joint was capable of predicting structure design of solid wood M&T joint furniture.In addition,the method of optimizing the solid wood M&T joint furniture was verified.It contributes to shorten the cycle of furniture structure design,save wood materials and reduce costs. |
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