console
function zk(){
let se = document.getElementById('select');
se.focus();
se.size=5;
showDropdown(se);
}
function showDropdown(element){
var event;
event = document.createEvent('MouseEvents');
event.initMouseEvent("mousedown", true, true, window, 0, 0, 0, 0, 0, false, false, false, false, 0, null);
element.dispatchEvent(event);
}
<select name="cars" id='select' >
<option value="volvo">Volvo</option>
<option value="saab">Saab</option>
<option value="fiat">Fiat</option>
<option value="audi">Audi</option>
</select>
<button onclick="zk()">展开</button>