tailieunhanh - The MEMS Handbook MEMS Applications (2nd Ed) - M. Gad el Hak Episode 1 Part 5

Tham khảo tài liệu 'the mems handbook mems applications (2nd ed) - m. gad el hak episode 1 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 4-18 MEMS Applications Buckling When a short column is loaded in compression the average compressive stress is calculated by simply dividing the load by the cross-sectional area as in Equation . However when the column is long and slender the situation is complicated by the possibility of static instability also known as lateral buckling. When loaded below the buckling threshold a column under a compressive load will get shorter while remaining essentially straight. After the buckling threshold is exceeded the column deflects normally to the axis of the column and the stress increases rapidly. These stresses can cause failure by rupture. The phenomenon of buckling is much different than that of bending. A beam will begin to bend as soon as any moment bending load is present. In contrast a column will not exhibit any lateral deflection until the critical or buckling load is reached. Above the critical load additional loading causes large increases in lateral deflection. Because of the tensile properties of polysilicon it is possible to design a column to buckle without exceeding the yield strength. If yield does not occur the column will return to its original straight position after the load is removed. If designed appropriately a buckling column can be used as an out-of-plane flexure Garcia 1998 . Buckling is a complex nonlinear problem and predicting the shape of the buckled structure is beyond the scope of this text. It is however covered in several references including Timoshenko and Gere 1961 Brush and Almroth 1975 Hutchinson and Koiter 1970 and Fang and Wickert 1994 . However the equation for predicting the onset of buckling is relatively straightforward. For a column with one end fixed and the other free to move in any direction . a cantilever the critical load to cause buckling is n2EI Fcr It is important to remember that the critical load for buckling cannot exceed the maximum force supported by the material. In other words if the load .