考虑损伤不同模量组合梁的纯弯曲研究

Pure Bending of Beam Composed of Different Moduli Materials with Damage Considered

根据考虑损伤的不同模量弹性理论,建立了考虑损伤的不同模量材料组合梁的弯曲基本方程。推导了梁的拉(压)应力、受拉区高度、损伤引起的中性轴偏移量和挠度的计算公式。应用数值计算方法,分别得到了有损与无损时梁的拉(压)应力与模量比的关系曲线,损伤引起的中性轴偏移量随载荷的变化规律,还比较了不同新增材料厚度下有损梁的拉(压)应力与模量比之间的关系曲线,比较了有损与无损梁的挠度曲线。这可为具有不同模量材料组合梁的截面设计提供一定的参考价值。

According to the elastic theory with different modulus considering material damage, the basic flexure equations of pure bending beam with different moduli material considering material damage are established. The calculation formulae of tension （compression） stress, tension zone height, neutral axis offsetcaused by damageand deflection of beam are derived. Using a numerical analysis method, the relationship curves between tension （compression） stress and the ratio of modulus are respectively achieved. The neutral axis offset caused by damage changing with the loadare obtained. The relationship curves between the tension （compression） stress and the ratio of modulus in the case of different new material thickness for the damaged beam are compared. The relationship curves between the deflections of the damage beam and non-damage beam are compared. These are useful for designing the beam section with different moduli combination.